student packet math in motion - idlewild & soakzone
TRANSCRIPT
STUDENT PACKET MATH IN MOTION
Math in Motion – Idlewild & SoakZone Copyright 2000
1
Your visit to Idlewild & SoakZone is an opportunity to
not only have fun, but learn about math and the use of
technology throughout the park. Use our Outdoor Classroom to broaden your appreciation of
Math in Motion.
STUDENT PACKET MATH IN MOTION
Math in Motion – Idlewild & SoakZone Copyright 2000
2
AANN AANNGGLLEE OONN DDIISSTTAANNCCEE
To determine the height of a ride, use a simple “protractor elevation finder.”
Have one student sight through the straw
(using the proper elevation given standing on the designated area) at the top of the ride.
Another student reads the angle on the protractor. The angle read is then subtracted from 90 degrees.
To calculate the height of the ride you will also need the distance (given to the students at the designated elevation sighting locations) between the students and the ride.
Tan =
H = d (tan )
height
distance
distance
(given)
height
Wild Mouse
Protractor
Straw
String
and
Weight
90 degrees
STUDENT PACKET MATH IN MOTION
Math in Motion – Idlewild & SoakZone Copyright 2000
3
0
10
20 0
30 0
4 0 0
6 0 0
50 0
9 0 0
80 0
70 0
Protractor Elevation Finder
1. Cut out the protractor including the dashed line section.
2. Trace the protractor part only on a piece of cardboard. (The back of a tablet works
nicely).
3. Glue or staple the cardboard to the back of the paper protractor.
4. Roll the top section around the straw and tape.
5. Punch a hole and tie a 9 inch string of heavy black thread through
the hole. On the other end tie a nut or fish sinker.
6. Follow the directions on the page titled “An Angle on Distance.”
Cardboard
d
STUDENT PACKET MATH IN MOTION
Math in Motion – Idlewild & SoakZone Copyright 2000
4
MMOOTTIIOONN
There are two basic types of motion. Motion that is uniform and accelerated motion.
For uniform motion, forces are balanced. There are no net or resulting forces. Under these
conditions calculating the velocity is straight forward.
Velocity = =
This velocity is an average for the trip.
Whenever an unbalanced force acts on an object, an acceleration is produced.
Acceleration = = or F = ma
F= Force, m= Mass, a= Acceleration
As you can see force and acceleration are related. Acceleration is the change in velocity over a
period of time. (How fast something is going faster.)
Acceleration = =
Acceleration occures anytime there is a change in velocity. For objects moving in a curved path,
velocity is changing even through speed may be constant. Velocity is a vector and therefore must
have speed and direction. If your direction is changing, like on the Super Round Up, then there is
an acceleration toward the center of the Super Round Up. This acceleration is called centripetal
acceleration.
Centripetal Acceleration = (velocity)2 ÷ radius V
Ac = Ac = Centripetal Acceleration
V = Velocity Ac
r = radius of the circle
In the case of an object spining in a circle, the size of the velocity (speed) is calculated by
measuring the time for one complete spin and dividing this into the circumfrance of the circle.
V = where (s) = distance = circumference
Distance traveled
Time of travel
s
t
Force
mass
Change in Velocity
Time
Change in V
t
V2
r
s
t
STUDENT PACKET MATH IN MOTION
Math in Motion – Idlewild & SoakZone Copyright 2000
5
If there is an acceleration there must be an unbalanced force producing it. The force causing the
circular motion is called centripetal force (Fc ). This force causes the object to change direction
thereby creating the acceleration in the same direction (towards the center).
As stated previously; F = ma
This is Newton’s 2nd
Law of motion and must apply to circular motion.
But note that: Fc = mac
ac = note the equation for ac
If we substitute in for (ac), we find the equation needed to calculate centripetal force.
Fc = mac becomes Fc =
This force is easy to see and understand if you swing a rubber stopper on the end of a string. You
can see your hand is producing the force which is transferred through the string to make the stopper
follow a circular path.
In the Super Round Up, the wall produces the centripetal force. This force keeps you moving in a
circular path by providing an acceleration on you toward the center. You, on the other hand, have
the impression that there is a force throwing you toward the wall. This is very similar to being in an
automobile at rest and the driver pushes the accelerator to the floor. If the car has a lot of
horsepower, you feel like you are being pushed back in the seat. In reality, the seat is accelerating
you forward. So, in the Super Round Up, the force you feel out against the wall, called centrifugal
force is a fictious force. You are reacting to the wall pushing you in!
Think of centripetal force as the action force and centrifugal force as the reaction force.
Remember, centrifugal force is considered to fictitious. It can only be observed in the acceleration
frame of reference.
These forces are also found on many other rides at Idlewild. Any ride which moves in a circular
motion or curved path will produce centripetal and centrifugal forces.
V2
r
V2
r
mv2
r
STUDENT PACKET MATH IN MOTION
Math in Motion – Idlewild & SoakZone Copyright 2000
6
Acceleration Finder The accelerometer is a device used to measure the acceleration of any moving object. For this project you will be observing the centripetal acceleration generated by the Carousel. Accelerometer Construction Materials Needed: Clear plastic bottle with lid that is closely the
same diameter of the bottle. Glue String or fishing line Fishing bobber (1”-2”dia.) the bigger your
bottle the bigger your bobber should be. Example: If the bottle is 3½“ in diameter the bobber should be about 1”-1½” in diameter.
Strong box tape Scissors Newspapers Water
Accelerometer Construction Directions: 1) Lay out your newspaper for easy
cleanup. 2) Attach the bobber to one end of the
string and hang it inside the bottle with the bobber just barely touching the bottom of the bottle.
3) Cut the string at the top of the bottle exactly at the same height as the lid. 4) Tape the string in the center of the lid with your box tape. Make sure the string is in the
exact center of your lid.
5) Place the bobber inside the bottle and close the top. The bobber should hang inside the
bottle without touching the bottom of the bottle. Approximately ½ inch from the bottom. 6) Fill the bottle with water approximately ½ inch from the top. Place the bobber inside the
bottle again and close the top tightly and securely. 7) Turn the bottle upside down and check for leaks. If it leaks, turn it back over and let it dry
where it leaked. You will need to seal the lid with glue with the assistance of your teacher.
cut
Bobb
er
String
Water
level
Lid
Bottle upside-down
Air gap
Accelerometer
Bottled
STUDENT PACKET MATH IN MOTION
Math in Motion – Idlewild & SoakZone Copyright 2000
7
AAVVEERRAAGGEE && PPEERRCCEENNTTAAGGEE
Average
Averages are obtained by adding the numbers in a set and dividing their sum by the total of the
elements involved.
For example, the average of 3 and 7 is 5
Calculated 3 + 7 = 10; 10 ÷ 2 (the total of elements in the set) is 5.
The average of 96, 89, 13, and 2 is (96 + 89 + 13 + 2) ÷ 4 = 50.
Percentage
The term “percentage” is derived from the Latin word per centum, meaning “per hundred,” this
term essentially represents fractions with the denominator of 100. Therefore, 35 percent (35%)
means the fraction 35/100.
To find the percentage of a number—for example, 20 percent of 40—20 must be changed to a
common fraction (20/100) or to a decimal (.20) and the figure multiplied by the whole (40); see
below
The percentage relationship of one number (5) to another (20), is calculated by dividing the first
number by the latter number then just multiplying this by 100; see below
5 ÷ 20 = .25, .25 x 100 = 25 percent or 25%
STUDENT PACKET MATH IN MOTION
Math in Motion – Idlewild & SoakZone Copyright 2000
8
Lengt Gravit Gravity: Acceleration of gravity (g) = 9.8 m / s2 Length: 1 inch = .0254 meters 1 foot = .3048 meters 1 mile = 1609.3 meters
1 meter = 3.28 ft Speed: Speed: 1 m/s = 2.23 mph
RREEFFEERREENNCCEE SSHHEEEETT
Circles: Circumfrence: C = D or 2r; where: = 3.14, D = diameter, r = radius
Area of a Circle = r2 Circumfrance of a circle = 2r
Triangles: c2 = a2 + b2 sin A = a/c cos A = b/c tan A = a/b
r
Angle
(degrees)
Tangent
Value 1 0.174
2 0.035
3 0.052
4 0.070
5 0.087
6 0.105
7 0.123
8 0.140
9 0.158
10 0.176
11 0.194
12 0.212
13 0.230
14 0.249
15 0.268
16 0.287
17 0.306
r
a c
b A
B
C
Angle
(degrees)
Tangent
Value 18 0.325
19 0.344
20 0.364
21 0.384
22 0.404
23 0.425
24 0.445
25 0.466
26 0.488
27 0.510
28 0.532
29 0.554
30 0.577
31 0.601
32 0.625
33 0.649
34 0.674
Angle
(degrees)
Tangent
Value 52 1.280
53 1.327
54 1.380
55 1.428
56 1.483
57 1.540
58 1.600
59 1.664
60 1.732
61 1.804
62 1.881
63 1.963
64 2.050
65 2.144
66 2.246
67 2.356
68 2.475
69 2.605
70 2.747
71 2.904
72 3.078
73 3.271
74 3.487
75 3.732
76 4.011
77 4.331
78 4.705
79 5.145
80 5.671
81 6.314
82 7.115
83 8.144
84 9.514
85 11.430
86 14.301
87 19.081
88 28.636
89 57.290
Angle
(degrees)
Tangent
Value 35 0.700
36 0.727
37 0.754
38 0.781
39 0.810
40 0.839
41 0.869
42 0.900
43 0.933
44 0.966
45 1.000
46 1.040
47 1.072
48 1.111
49 1.150
50 1.192
51 1.235
System o System of Measurment: System Length Mass Time Force Velocity Acceleration Metric (MKS)
meter (m) kg sec newton (N) m/s m/s/s
Metric (CGS)
cm gram sec dyne cm/s cm/s/s
English (FPS)
ft slug sec Pound (lb) ft/s ft/s/s
STUDENT PACKET MATH IN MOTION
Math in Motion – Idlewild & SoakZone Copyright 2000
9
STUDENT PACKET MATH IN MOTION
Investigation #1 Wild Mouse Coaster – Idlewild & SoakZone Copyright 2000 10
IINNVVEESSTTIIGGAATTIIOONN ## 11
WWIILLDD
MMOOUUSSEE
Hidden among the trees, Idlewild’s Wild Mouse is a modern version of the classic Wild
Mouse roller coasters, featuring mouse-shaped cars carrying four riders each. Once the
cars are hoisted to the top of the lift hill, they must follow the sudden twists, dips, and
hills that will lead them back to the station.
The velocity at the base of the Wild Mouse first drop is represented by the formula:
V= gh (squared)
Using the method discussed in the Student Activity Guidebook “An Angle on Distance”,
find the height of the Wild Mouse at several points of the first drop. (Use the markers on
the ride and the designated sighting location to make your calculations.) The sighting
location is just after entering the entrance line to the ride. Follow the path until you pass
some rocks making up the entrance line. When the rocks end, look to your left. The tree
is located approximately 3 meters to the left marked with a red bull’s eye.
STUDENT PACKET MATH IN MOTION
Investigation #1 Wild Mouse Coaster – Idlewild & SoakZone Copyright 2000 11
1. Height of column A from the ground:
Height of point A = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the Wild Mouse = height from above + height of your eye.
Height of point A = ____________ + _____________ = ______________ meters
Distance from Track = 14.63 meters
The height of your eye from the
ground _____________ meters
Height
Sight to the top of column while
standing in front of the large
marked tree.
= ___________ degrees
(Ground
Level) Stand at the red bull’s-eye to use the correct distance given.
Column
A
STUDENT PACKET MATH IN MOTION
Investigation #1 Wild Mouse Coaster – Idlewild & SoakZone Copyright 2000 12
2. Height of column B from the ground:
Height of point B = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the Wild Mouse = height from above + height of your eye.
Height of point B= ____________ + _____________ = ______________ meters
Distance from Track = 11.27 meters
The height of your eye from the
ground _____________ meters
Height
Sight to the top of column while
standing in front of the large
marked tree.
= ___________ degrees
(Ground Level)
Stand at the red bull’s-eye to use the correct distance given.
Column
B
STUDENT PACKET MATH IN MOTION
Investigation #1 Wild Mouse Coaster – Idlewild & SoakZone Copyright 2000 13
3. Height of column C from the ground:
Height of point C = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the Wild Mouse = height from above + height of your eye.
Height of point C = ____________ + _____________ = ______________ meters
Distance from Track = 9.44 meters
The height of your eye from the
ground _____________ meters
Height
Sight to the top of column while
standing in front of the large
marked tree.
= ___________ degrees
(Ground Level)
Stand at the red bull’s-eye to use the correct distance given.
Column
C
STUDENT PACKET MATH IN MOTION
Investigation #1 Wild Mouse Coaster – Idlewild & SoakZone Copyright 2000 14
4. Height of column D from the ground:
Height of point D = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the Wild Mouse = height from above + height of your eye.
Height of point D = ____________ + _____________ = ______________ meters
Distance from Track = 10.05 meters
The height of your eye from the
ground _____________ meters
Height
Sight to the top of column while
standing in front of the large
marked tree.
= ___________ degrees
(Ground Level)
Stand at the red bull’s-eye to use the correct distance given.
Column
D
STUDENT PACKET MATH IN MOTION
Investigation #1 Wild Mouse Coaster – Idlewild & SoakZone Copyright 2000 15
5. Height of column E from the ground:
Height of point E = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the Wild Mouse = height from above + height of your eye.
Height of point E = ____________ + _____________ = ______________ meters
Distance from Track = 12.80 meters
The height of your eye from the
ground _____________ meters
Height
Sight to the top of column while
standing in front of the large
marked tree.
= ___________ degrees
(Ground Level)
Stand at the red bull’s-eye to use the correct distance given.
Column
E
STUDENT PACKET MATH IN MOTION
Investigation #1 Wild Mouse Coaster – Idlewild & SoakZone Copyright 2000 16
6. Height of column F from the ground:
Height of point F = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the Wild Mouse = height from above + height of your eye.
Height of point F = ____________ + _____________ = ______________ meters
Distance from Track = 16.15 meters
The height of your eye from the
ground _____________ meters
Height
Sight to the top of column while
standing in front of the large
marked tree.
= ___________ degrees
(Ground Level)
Stand at the red bull’s-eye to use the correct distance given.
Column
F
STUDENT PACKET MATH IN MOTION
Investigation #1 Wild Mouse Coaster – Idlewild & SoakZone Copyright 2000 17
7. Height of column G from the ground:
Height of point G = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the Wild Mouse = height from above + height of your eye.
Height of point G = ____________ + _____________ = ______________ meters
Distance from Track = 20.11 meters
The height of your eye from the
ground _____________ meters
Height
Sight to the top of column while
standing in front of the large
marked tree.
= ___________ degrees
(Ground Level)
Stand at the red bull’s-eye to use the correct distance given.
Column
G
STUDENT PACKET MATH IN MOTION
Investigation #1 Wild Mouse Coaster – Idlewild & SoakZone Copyright 2000 18
8. Height of column H from the ground:
Height of point H = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the Wild Mouse = height from above + height of your eye.
Height of point H = ____________ + _____________ = ______________ meters
Distance from Track = 24.38 meters
The height of your eye from the
ground _____________ meters
Height
Sight to the top of column while
standing in front of the large
marked tree.
= ___________ degrees
(Ground Level)
Stand at the red bull’s-eye to use the correct distance given.
Column
H
STUDENT PACKET MATH IN MOTION
Investigation #1 Wild Mouse Coaster – Idlewild & SoakZone Copyright 2000 19
9. Height of the column A from the height of the lowest column_________?:
Therefore the height of the first drop from the bottom of the drop would be the distance
between theses two points.
Height of Point A – height of point ______? = height of the first drop from the bottom of
the drop.
______________ – ______________ = ___________________
10. Velocity of the first drop:
Now that you know the height of the drop at it’s highest point and lowest point, use the
velocity formula at the beginning of the question to calculate the velocity at point B in the
diagram with the help of knowing the speed of gravity.
Speed of Gravity (g) = 9.8 m / s2
(h) = height of the ride
V = gh
= (9.8 m/s2)(_________)
= ________ = ___________
11. On the chart below, graph the heights of each column. Then draw a line
representing the track the cars run on. Each column is approximately 5 meters apart from
one another.
Investigation #2 Highest of the High – Idlewild & SoakZone Copyright 2000 20
IINNVVEESSTTIIGGAATTIIOONN ##22
HHIIGGHHEESSTT OOFF TTHHEE HHIIGGHH
Using the method discussed in the student Activity Guidebook “An Angle on
Distance”, find the height of the Wild Mouse at its highest and lowest points of the first
drop. (Use the markers on the ride and the designated sighting location to make your
calculations.)
12. Height of the Wild Mouse:
Height of the ride = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the ride = height from above + height of your eye from the bridge + the height
of the bridge (1.82 meters).
Height of the ride = ____________ + _____________ = ______________ meters
Distance from Ride: 19.81 meters
The height of your
eye from the ground
_____________ meters
Height
Sight to the top marker from
the red bull’s-eye on the
bridge crossing the creek.
The marker is located on the
wooden railing on the wild
mouse side of the bridge.
= ___________ degrees
(Ground Level)
Stand at the red bull’s-eye to use the correct distance given.
Investigation #2 Highest of the High – Idlewild & SoakZone Copyright 2000 21
13. Height of the Rafters Run:
Height of the ride = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the ride = height from above + height of your eye.
Height of the ride = ____________ + _____________ = ______________ meters
Distance from Ride: 76.20 meters
The height of your
eye from the ground
_____________ meters
Height
Sight to the top of the roof from
the red bull’s-eye located near the
exit of the ride.
= ___________ degrees
(Ground Level)
Stand at the red bull’s-eye to use the correct distance given.
Investigation #2 Highest of the High – Idlewild & SoakZone Copyright 2000 22
14. Height of the Ferris Wheel:
Height of the ride = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the ride = height from above + height of your eye.
Height of the ride = ____________ + _____________ = ______________ meters
Distance from Ride: 14.02 meters
The height of your
eye from the ground
_____________ meters
Height
Sight to the top of the ride from
the red bull’s-eye located near
the entrance of the ride.
= ___________ degrees
(Ground Level)
Stand at the red bull’s-eye to use the correct distance given.
Investigation #2 Highest of the High – Idlewild & SoakZone Copyright 2000 23
15. Height of the Jumpin’ Jungle Tree House:
Height of the ride = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the ride = height from above + height of your eye.
Height of the ride = ____________ + _____________ = ______________ meters
Distance from Ride: 21.64 meters
The height of your
eye from the ground
_____________ meters
Height
Sight to the top of the roof
from the red bull’s-eye
located near the entrance of
the ride.
= ___________ degrees
(Ground Level)
Stand at the red bull’s-eye to use the correct distance given.
Investigation #2 Highest of the High – Idlewild & SoakZone Copyright 2000 24
16. Height of the Rollo Coaster:
Height of the ride = distance away ( Tan )
Height = _____________ ( ___________ ) = __________________ meters
Don’t forget the height of your eye
Height of the ride = height from above + height of your eye.
Height of the ride = ____________ + _____________ = ______________ meters
Distance from Ride: 16.76 meters
The height of your
eye from the ground
_____________ meters
Height
Sight to the top of the railing
from the red bull’s-eye
located near the exit of the
ride.
= ___________ degrees
(Ground Level)
Stand at the red bull’s-eye to use the correct distance given.
Investigation #2 Highest of the High – Idlewild & SoakZone Copyright 2000 25
17. Graph your results.
Draw a line to represent each ride in order of height.
Label the ride and it’s height.
STUDENT PACKET MATH IN MOTION
Investigation #3 Centripetal Force & Centripetal Acceleration – Idlewild & SoakZone Copyright 2000 26
IINNVVEESSTTIIGGAATTIIOONN 33
CCEENNTTRRIIPPEETTAALL FFOORRCCEE &&
CCEENNTTRRIIPPEETTAALL AACCCCEELLEERRAATTIIOONN
Carousel (Accelerometer required) Safety Precautions: You MUST stay between the inner and outer horses AT ALL TIMES while the ride is moving. Do not walk around the ride while in motion. Failure to follow this rule could result in personal injury. It will also result in your removal from the ride and possible loss of your rider’s pass for the remainder of the day. Directions:
1. Place the accelerometer lid side down on the deck of the carousel behind an inside horse.
2. Stand beside the accelerometer and look down so that one eye is directly over the bobber. Notice the location of the bobber.
3. As the ride begins to move, notice the motion of the bobber. 4. Take note of where the bobber is in relation to the center of the accelerometer. 5. After observing the accelerometer for one ride move behind an outside horse after
the ride stops. 6. Once again place the accelerometer on the deck of the carousel.
STUDENT PACKET MATH IN MOTION
Investigation #3 Centripetal Force & Centripetal Acceleration – Idlewild & SoakZone Copyright 2000 27
7. Notice where the bobber is in relation to the center of the accelerometer. Continue watching the accelerometer until the carousel has nearly stopped.
8. Once the ride has come to a complete stop you may step off the platform.
STUDENT PACKET MATH IN MOTION
Investigation #3 Centripetal Force & Centripetal Acceleration – Idlewild & SoakZone Copyright 2000 28
Questions:
A. What happened to the bobber as the carousel began to move?
B. While riding by the inside horse, where was the bobber (in relation to the center of the accelerometer)?
C. While riding by the outside horse, where was the bobber (in relation to the center of the accelerometer)?
D. By which horse, the inner or outer, did the bobber move further away from center?
E. Based upon your observations, where is the centripetal acceleration greatest? Why?
STUDENT PACKET MATH IN MOTION
Investigation #3 Centripetal Force & Centripetal Acceleration – Idlewild & SoakZone Copyright 2000 29
1. Which number position on the diagram would you have the greatest speed? _______
2. Which number position on the diagram would you have the smallest speed? _______
3. At position A; draw an arrow representing the
velocity at that instant. Also draw an arrow
that represents the acceleration. (Label them v
and a)
4. At position B; draw an arrow representing the
velocity at that instant. Also draw an arrow
that represents the acceleration. (Label them v
and a)
5. From the radius, calculate the circumference
of the Carousel.
(Note: circumference = times 2r
where = 3.14 and r = radius.)
Circumference = _________________
6. Using your watch or stopwatch,
measure how long it takes to make
one trip around. (You may find it easier to time 5 trips and divided by five. Note: some
rides take a minute or two to reach full speed.)
One trip = _________________
7. The speed will be the distance traveled (circumference) divided by the time for that
distance (period). At what position would you have the greatest centripetal acceleration
towards the center? (1, 2 or 3)? Calculate them.
Velocity (V) = =
Centripetal Acceleration (Ac) =
Note: The overall radius of the carousel is 7.16m.
1 2 3
A
B
Carousel
Platform
Top View
#1 r = 4.72 m
#2 r =
5.48 m #3 r =
6.55 m
distance
time circumference
period
V2
r
STUDENT PACKET MATH IN MOTION
Investigation #3 Centripetal Force & Centripetal Acceleration – Idlewild & SoakZone Copyright 2000 30
Super Round Up
1. When spinning, the wall of the Super Round Up pushes on you to make you change
direction. This force on you is called _______________________________.
2. In the moving frame of reference, you feel that there is a force pushing you outward
against the wall. This force, which is fictitious, is called
________________________.
3. From the radius, calculate the circumference of the Round Up. (Note: circumference = times 2r
where = 3.14 & r = radius.)
Circumference = _________________
4. Using your watch or stopwatch, measure how long it takes to make one trip around. (You
may find it easier to time 5 trips and divided by five. Note: some rides take a minute or
two to reach full speed.)
One trip = _________________
5. The speed will be the distance traveled (circumference) divided by the time for that
distance (period). What is the centripetal acceleration of the ride?
Velocity (V) = =
Centripetal Acceleration (Ac) =
distance
time circumference
period
V2
r
Radius (r) = 6.09 meters
STUDENT PACKET MATH IN MOTION
Investigation #3 Centripetal Force & Centripetal Acceleration – Idlewild & SoakZone Copyright 2000 31
Next… Ride several rides and observe the effects on your body.
Explain what would be the centripetal force used by the ride to give you centripetal
acceleration for each ride.
Take notes and explain why one ride may react differently as compared to another. What
might be the reasons for this?
STUDENT PACKET MATH IN MOTION
Investigation #4 Speed or Velocity – Idlewild Park 2000 32
IINNVVEESSTTIIGGAATTIIOONN 44 SSPPEEEEDD OORR VVEELLOOCCIITTYY
Ferris Wheel
1. From the radius, calculate the circumference of the Ferris
Wheel.
(Note: circumference = times 2r
where = 3.14 and r = radius.)
Circumference = _________________
2. Using your watch or stopwatch, measure how long it
takes to make one trip around. (You may find it easier to
time 5 trips and divided by five. Note: some rides take a
minute or two to reach full speed.)
One trip = _________________
3. Calculate the speed of rotation. The speed
will be the distance traveled
(circumference) divided by the time for
that distance (period).
V = =
=
= _________________
4. Graph your results.
distance
time
circumference
period
Radius (r) = 7.62 meters
STUDENT PACKET MATH IN MOTION
Investigation #4 Speed or Velocity – Idlewild Park 2000 33
Carousel
1. From the radius, calculate the
circumference of the Carousel.
(Note: circumference = times 2r
where = 3.14 & r = radius.)
Circumference =
_________________
2. Using your watch or stopwatch,
measure how long it takes to make
one trip around. (You may find it
easier to time 5 trips and divided by five. Note: some rides take a minute or two to reach full speed.)
One trip = _________________
3. Calculate the speed of rotation. The speed
will be the distance traveled (circumference)
divided by the time for that distance (period).
V = =
=
V = ______________
4. Graph your results.
distance
time
circumference
period
Radius (r) = 7.16 meters
STUDENT PACKET MATH IN MOTION
Investigation #4 Speed or Velocity – Idlewild Park 2000 34
Flying Aces
1. From the radius, calculate the circumference of the Flying Aces.
(Note: circumference = times 2r where = 3.14 and r = radius.)
Circumference = _________________
2. Using your watch or stopwatch, measure how long it takes to make one trip around. (You may
find it easier to time 5 trips and divided by five. Note: some rides take a minute or two to reach
full speed.)
One trip = approx.
_________________seconds.
3. Calculate the speed of rotation.
The speed will be the distance
traveled (circumference) divided
by the time for that distance
(period).
V = =
=
V = ______________
4. Graph your results.
distance
time
circumference
period
Radius (r) = 15.85 meters
Timing the Flying Aces: Find a spot along the outside perimeter fence (outside the ride area). Select one of the ten 2-seated cars to observe. When it appears that the ride has reached full speed, start timing when your selected car passes the center of the ride. Stop it once that same car passes the center of the ride again. Good Luck.
STUDENT PACKET MATH IN MOTION
Investigation #4 Speed or Velocity – Idlewild Park 2000 35
Super Round Up
1. From the radius, calculate the
circumference of the Super Round Up.
(Note: circumference = times 2r
where = 3.14 & r = radius.)
Circumference = _________________
2. Using your watch or stopwatch,
measure how long it takes to make one trip around. (You may find it easier to time 5 trips and
divided by five. Note: some rides take a minute or two to reach full speed.)
One trip = approx. ______ seconds
3. Calculate the speed of rotation. The speed
will be the distance traveled (circumference)
divided by the time for that distance (period).
V = =
=
V = ______________
4. Graph your results.
distance
time
circumference
period
Radius (r) = 6.09 meters
STUDENT PACKET MATH IN MOTION
Investigation #4 Speed or Velocity – Idlewild Park 2000 36
Howler (located in Hootin' Holler') The Howler, while in full motion, has a radius (r) of 9.89 meters.
From the radius, calculate the
circumference of the Howler in full motion.
(Note: circumference = times 2r
where = 3.14 and r = radius.)
Circumference = _________________
Using your watch or stopwatch, measure how long it takes to make
one trip around. (You may find it easier to time 5 trips and divide
by five. Note: some rides take several seconds to reach full speed.)
One trip = approx. __________ seconds
Calculate the speed of rotation. The speed
will be the distance traveled
(circumference) divided by the time for
that distance (period).
V = =
=
V = ____________
Graph your results.
distance
time
circumference
period
Radius (r) = 3.35 meters
Timing the Howler To make things easier stand to the left side of the little shed where the ride operator sits facing the ride. (You must be outside the ride area). Select one of the six 4-seated ride cars to observe. When it appears that the ride has reached full speed, start timing when your selected car passes the center of the ride. Stop it once that same car passes the center of the ride again. Good Luck.
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 37
IINNVVEESSTTIIGGAATTIIOONN ## 55
RROOLLLLOO CCOOAASSTTEERR
The Rollo Coaster was built by the Philadelphia Toboggan Company and opened to Idlewild’s Guests in 1938. It’s two trains carry riders up and down along a wooded hillside, only to turn around in a swooping curve and return back towards the station. The rides last approximately 70 seconds on a track that runs nearly 1400 feet. The Rollo Coaster has been named an American Coaster Enthusiasts Classic Coaster.
Please keep the following in mind while doing your calculation: Some days the Rollo Coaster operates with two coaster trains. If you are visiting on one of these days, please know that one coaster normally runs a little faster than the other. Also, rain tends to make the coasters run a little faster and the heavier or larger group of people in a coaster will cause it to run faster, while cold temperatures cause casters to run slower.
Note: You must be 48 inches tall to ride or be accompanied by an adult.) This investigation will require you to ride the Rollo Coaster. Because of this fact, one individual would have to ride the coaster between 15 and 36 times to obtain the necessary information, which we do not suggest. Therefore, it is recommended that this investigation should be done as a TEAM, in groups of 5 to 10 individuals, sharing the findings.
RRRooollllllooo CCCoooaaasssttteeerrr
Blueprint
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 38
1. Using a stopwatch or the second hand on your watch, time how long it takes the train to
give one ride. The train travels 411.48 meters from when the train starts moving until it
stops to unload. Start timing the train as soon as it begins to move out of the station until
it stops completely at the back of the station to unload the people. Make several
measurements and find the average. All Start and stop points are marked on the ride.
Some calculations may require riding or observing from the midway. (If two trains are in
operation, be sure to clock the same train entering the station)
Trip Seconds
Coaster
number
circle one
Weather - rain,
cold, warm, dry circle all that apply
Fully train or
partially full train
circle one
# 1
1 or 2 R – C – W - D F or P
# 2
1 or 2 R – C – W – D F or P
# 3
1 or 2 R – C – W – D F or P
Average
Hint: Average for one trip = total seconds of all trips
combined total number of trips
Calculate the average speed of the Rollo Coaster.
Velocity calculation here.
V = = =
Rollo Coaster
Blueprint
Start
# 1 Stop
# 8
distance
time
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 39
Calculate the average speed of sections 1 through 7.
2. Time how long it takes the train to travel 64 meters from point 1 to point 2.
Trip Seconds
Coaster
number
circle one
Weather - rain,
cold, warm, dry circle all that apply
Fully train or
partially full train
circle one
# 1
1 or 2 R – C – W - D F or P
# 2
1 or 2 R – C – W – D F or P
# 3
1 or 2 R – C – W – D F or P
Average
Hint: Average for one trip = total seconds of
all trips combined total number of trips
Calculate the average speed of section 1.
Velocity calculation here.
V = = =
Rollo Coaster Blueprint
Time:
____________
Start
# 1
Stop
# 2
distance
time
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 40
3. Time how long it takes the train to travel 59.74 meters from point 2 to point 3.
Trip Seconds
Coaster
number
circle one
Weather - rain,
cold, warm, dry circle all that apply
Fully train or
partially full train
circle one
# 1
1 or 2 R – C – W - D F or P
# 2
1 or 2 R – C – W – D F or P
# 3
1 or 2 R – C – W – D F or P
Average
Hint: Average for one trip = total seconds of
all trips combined total number of trips
Calculate the average speed of section 2.
Velocity calculation here.
V = = =
Rollo Coaster Blueprint
Start
# 2 Stop
# 3
distance
time
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 41
4. Time how long it takes the train to travel 56.69 meters from point 3 to point 4.
Trip Seconds
Coaster
number
circle one
Weather - rain,
cold, warm, dry circle all that apply
Fully train or
partially full train
circle one
# 1
1 or 2 R – C – W - D F or P
# 2
1 or 2 R – C – W – D F or P
# 3
1 or 2 R – C – W – D F or P
Average
Hint: Average for one trip = total seconds of
all trips combined total number of trips
Calculate the average speed of section 3.
Velocity calculation here.
V = = =
Rollo Coaster Blueprint
Start
# 3
Stop
# 4
distance
time
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 42
5. Time how long it takes the train to travel 43.89 meters from point 4 to point 5.
Trip Seconds
Coaster
number
circle one
Weather - rain,
cold, warm, dry circle all that apply
Fully train or
partially full train
circle one
# 1
1 or 2 R – C – W - D F or P
# 2
1 or 2 R – C – W – D F or P
# 3
1 or 2 R – C – W – D F or P
Average
Hint: Average for one trip = total seconds of
all trips combined total number of trips
Calculate the average speed of section 4.
Velocity calculation here.
V = = =
Rollo Coaster Blueprint
Start
# 4 Stop
# 5
distance
time
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 43
6. Time how long it takes the train to travel 64.61 meters from point 5 to point 6.
Trip Seconds
Coaster
number
circle one
Weather - rain,
cold, warm, dry circle all that apply
Fully train or
partially full train
circle one
# 1
1 or 2 R – C – W - D F or P
# 2
1 or 2 R – C – W – D F or P
# 3
1 or 2 R – C – W – D F or P
Average
Hint: Average for one trip = total seconds of
all trips combined total number of trips
Calculate the average speed of section 5.
Velocity calculation here.
V = = =
Rollo Coaster Blueprint
Start
# 5
Stop
# 6
distance
time
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 44
7. Time how long it takes the train to travel 63.40 meters from point 6 to point 7.
Trip Seconds
Coaster
number
circle one
Weather - rain,
cold, warm, dry circle all that apply
Fully train or
partially full train
circle one
# 1
1 or 2 R – C – W - D F or P
# 2
1 or 2 R – C – W – D F or P
# 3
1 or 2 R – C – W – D F or P
Average
Hint: Average for one trip = total seconds of
all trips combined total number of trips
Calculate the average speed of section 6.
Velocity calculation here.
V = = =
Rollo Coaster Blueprint
Start
# 6
Stop
# 7
distance
time
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 45
8. Time how long it takes the train to travel 63.40 meters from point 7 to point 8.
Trip Seconds
Coaster
number
circle one
Weather - rain,
cold, warm, dry circle all that apply
Fully train or
partially full train
circle one
# 1
1 or 2 R – C – W - D F or P
# 2
1 or 2 R – C – W – D F or P
# 3
1 or 2 R – C – W – D F or P
Average
Hint: Average for one trip = total seconds of
all trips combined total number of trips
Calculate the average speed of section 7.
Velocity calculation here.
V = = =
Rollo Coaster Blueprint
Start
# 7
Stop
# 8
distance
time
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 46
Calculate were the coaster reaches the greatest speed.
Sections A – B, C – D, or E – F ?
9. Time how long it takes the train to travel 12.19 meters from point A to point B.
Trip Seconds
Coaster
number
circle one
Weather - rain,
cold, warm, dry circle all that apply
Fully train or
partially full train
circle one
# 1
1 or 2 R – C – W - D F or P
# 2
1 or 2 R – C – W – D F or P
# 3
1 or 2 R – C – W – D F or P
Average
Hint: Average for one trip = total seconds of
all trips combined total number of trips
Calculate the average speed of segment A – B.
Velocity calculation here.
V = = =
Rollo Coaster Blueprint
Start
# A
Stop
# B
distance
time
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 47
10. Time how long it takes the train to travel 12.19 meters from point C to point D.
Trip Seconds
Coaster
number
circle one
Weather - rain,
cold, warm, dry circle all that apply
Fully train or
partially full train
circle one
# 1
1 or 2 R – C – W - D F or P
# 2
1 or 2 R – C – W – D F or P
# 3
1 or 2 R – C – W – D F or P
Average
Hint: Average for one trip = total seconds of
all trips combined total number of trips
Calculate the average speed of segment C – D.
Velocity calculation here.
V = = =
Rollo Coaster Blueprint
Start
# C
Stop
# D
distance
time
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 48
11. Time how long it takes the train to travel 12.19 meters from point E to point F.
Trip Seconds
Coaster
number
circle one
Weather - rain,
cold, warm, dry circle all that apply
Fully train or
partially full train
circle one
# 1
1 or 2 R – C – W - D F or P
# 2
1 or 2 R – C – W – D F or P
# 3
1 or 2 R – C – W – D F or P
Average
Hint: Average for one trip = total seconds of
all trips combined total number of trips
Calculate the average speed of segment E – F.
Velocity calculation here.
V = = =
Rollo Coaster Blueprint
Start
# E
Stop
# F
distance
time
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 49
12. What section of track has the greatest velocity and the least velocity?
(Mark your answer on the blueprint below.)
13. What segment of track has the greatest velocity?
(Mark your answer on the blueprint below.)
14. Which half of the ride is faster (do not include section 1)?
First half or Second half
Sections 2 – 5 Sections 5 – 8?
15. If you visited on a day that 2 coaster trains were operating, which coaster was fastest?
(1 or 2) (Note: Many days only 1 train operates.)
Rollo Coaster Blueprint
STUDENT PACKET MATH IN MOTION
Investigation #5 Rollo Coaster – Idlewild & SoakZone 2000 50
16. If it were raining, how would this effect your calculations?
17. If it were cold, how would your calculations be effected?
18. If it were cold and raining, how would this effect the ride?
19.Compare you calculations with the rest of the class. Who clocked the fastest coaster
and what number was it?
STUDENT PACKET MATH IN MOTION
Investigation #6 Percentages, Capacity & Averages – Idlewild & SoakZone Copyright 2000 51
IINNVVEESSTTIIGGAATTIIOONN ## 66
PPEERRCCEENNTTAAGGEESS,, CCAAPPAACCIITTYY && AAVVEERRAAGGEESS
Potato
Patch
1. Find the average length of a Potato Patch fry.
Get a complimentary cup of “experiment size” fries at the Mineshaft Kitchen,
Potato Patch Fries stand. Go through the line and show the cashier your
worksheet for this activity.
Total Length of Fries Total Number of all Fries combined = Average Length
Note: If you find a fry shorter than 1 inch, do not count it in the total number of fries but do add it to the total length.
2. How many servings of fries would it take to follow the entire track
of the Wild Mouse (1,640 feet) if the fries were laid end to end?
Total Length of the Track Total Fry Length (Total Length of all Fries combined) = Amount of servings required
STUDENT PACKET MATH IN MOTION
Investigation #6 Percentages, Capacity & Averages – Idlewild & SoakZone Copyright 2000 52
Happy
Goblet
Game
(Located in Olde Idlewild)
1. At the Happy Goblet Game, calculate the percent chance of winning:
(Chance of winning = Total Amount of winners Total number of Chances)
a) Any prize
b) A red goblet prize
c) A green goblet prize
d) Percent chance of winning any prize
STUDENT PACKET MATH IN MOTION
Investigation #6 Percentages, Capacity & Averages – Idlewild & SoakZone Copyright 2000 53
Rising Waters (Located in Olde Idlewild)
1. Calculate the amount of profit earned by the park per day on the
Rising Waters Game if the game ran continuously for one day and it
averaged 7 players each time the game was played.
* One day = 10 hrs. * Idle time between games = 7 minutes
a. Duration of one game in seconds_______________________________.
b. Games per hour _____________________.
c. Cash collected per game. ________________________________.
d. Games per day _____________________.
e. Gross profit per day _______________.
STUDENT PACKET MATH IN MOTION
Investigation #6 Percentages, Capacity & Averages – Idlewild & SoakZone Copyright 2000 54
Wild
Mouse
1. Calculate the average duration of one complete trip from the time the car leaves the
station until it leaves a second time. (Average three trips)
2. Estimate the maximum capacity of people the ride can accommodate with 6 cars in
operation in one day. One day = 11 hrs
3. Estimate the average capacity of people the ride can accommodate with 6 cars in
operation in one day. One day = 11 hrs
(To find the average capacity the Wild Mouse can accommodate in one day, count up
the number of people in six different cars. Now divide that number by six. Use this
number instead of 4 for the amount of people each car can hold.)
STUDENT PACKET MATH IN MOTION
Investigation #6 Percentages, Capacity & Averages – Idlewild & SoakZone Copyright 2000 55
Balloon
Race
1. Estimate the total number of light bulbs on the entire ride.
(Hint: each balloon top is made up of four identical panels that make the balloon.)
2. Estimate the percentages of each color used to paint the Balloon Race ride.
(Note: Do not include the base of the ride.)
STUDENT PACKET MATH IN MOTION
Investigation #6 Percentages, Capacity & Averages – Idlewild & SoakZone Copyright 2000 56
Bubbling Springs Ball Crawl
(Located in Jumpin’ Jungle)
1. How many balls are in the Bubbling Springs Ball Crawl?
Octagon shape (18’ per side of octagon) 2 feet deep
Diameter of balls - two sizes: 73 mm @ 81 per cubic foot 80 mm @ 67 per cubic foot