unit plan - grade 11 u...

Unit Plan - Grade 11 U Kinematics

OVERVIEW L LESSON TITLES (TOPICS/THEMES)

Kinematics is the branch of classical mechanics that describes the motion of objects

[1]. In this unit, students will explore the

physics of motion in one and two-dimensions. Students will

learn new concepts of scalars and vectors, differential properties of motion such as velocity and acceleration, as well as deriving

algebraic equations representing the relationship between the

different variables of motion.

Students will also explore the importance of kinematics in real-life applications. Students will spend 3 periods conducting

experimental work to strengthen their understanding of the new

concepts taught in this unit.

[1] Joseph Stiles Beggs (1983). Kinematics. Taylor & Francis.

p. 1

1 Distance, Position, and Displacement

2 Speed and Velocity

3 Acceleration

4 Comparing Graphs of Linear Motion

5 Five Key Equations for Motion with Uniform Acceleration

6 Acceleration Near Earth’s Surface

7 Experiment: Ticker Tape

8 Motion in Two Dimension

9 Projectile Motion – Day 1

10 Projectile Motion – Day 1

11 Experiment – Day 1: Projectile Motion Experiment

12 Experiment – Day 2: Projectile Motion Experiment & Write up

13 Motion in Our Lives

14

Unit Review

15 Unit Summative Assessment

http://books.google.com/books?id=y6iJ1NIYSmgC&printsec=frontcover&dq=kinematics&lr=&as_brr=0&sig=brRJKOjqGTavFsydCzhiB3u_8MA#PPA1,M1

OVERALL EXPECTATIONS L SPECIFIC EXPECTATIONS LEARNING GOALS

B1. Analyse technologies that apply

concepts related to kinematics, and

assess the technologies’ social and environmental impact;

B2. Investigate, in qualitative and quantitative terms, uniform and non-

uniform linear motion, and solve

related problems;

B3. Demonstrate an understanding of

uniform and non-uniform linear

motion, in one and two dimensions

1 B2.1, B3.2

Students will be able to:

Explain how distance, position, and displacement are different

Explain the difference between scalars and vectors

Calculate the displacement of an object algebraically and by a

vector scalar diagram

2 B2.1, B3.1, B3.2 Students will be able to:

Explain how speed and velocity are different

Explain the relationship between velocity, displacement, and

time

Determine velocity from position-time graph


Explain the relationship between acceleration, velocity,

displacement, and time

Determine acceleration from velocity-time graph

Determine the difference between average velocity and

instantaneous velocity

4 B2.2, B3.1 Students will be able to:

Obtain information from position-time, velocity-time, and

acceleration-time graphs

Realize that given one type of motion graph, they can construct

a different type of graph


Derive the 5 key equations of motion

Solve uniform velocity and uniform acceleration using algebraic

methods


Understand that the symbol of g is used to represent the

acceleration due to gravity Describe how the acceleration due to

gravity affects the motion of objects close to the surface of Earth

Describe how the acceleration due to gravity affects the motion

of objects close to the surface of Earth (g = 9.8 m/s2)

Understand the concept of terminal velocity


Construct ticker tape experiment to explain the motion of a

moving car

Construct and obtain information from motion graphs

Present a scientifically written lab report


Describe how to determine total displacement in 2-deminsions

by scalar diagram and by component method

Solve problems that involve moving in 2-dimensions


Determine the factors affecting projectile motion (angle,

launching velocity, initial height, gravity, etc.)

10

B1.1, B2.8, B3.3 Students will be able to:

Understand that projectile motion consists of independent

horizontal and vertical motions

Understand that the horizontal and vertical motions take the

same amount of time

Understand that projectiles move horizontally at a constant

velocity, and undergo uniform acceleration vertically

Solve problems related to the horizontal and vertical

components of motion of a projectile using kinematic equations

(determine the range, maximum height, and time of flight foe a projectile’s motion)


Use a projectile launcher to examine the properties of projectile

motion

Experiment the various factors that affect projectile motion


Use a projectile launcher to examine the properties of projectile

motion

Experiment the various factors that affect projectile motion

Write a scientific lab report


Asses the social and environmental impacts of a technology that

applies kinematics concepts

14 B1.1, B2.1, B2.2, B2.3, B2.4,

B2.5, B2.6, B2.7, B2.8, B2.9,

B3.1, B3.2, B3.3

Students will be able to:

Determine the level of their understanding of kinematics

Ask for help if needed

15 B1.1, B2.1, B2.2, B2.3, B2.4,

B2.5, B2.6, B2.7, B2.8, B2.9, B3.1, B3.2, B3.3

Students will be:

At the expected level of understanding kinematics

Big Question L LITTLE BIG QUESTIONS LESSON OVERVIEW

How do we measure motion?

What are the applications of kinematics?

1 What is the difference between a scalar and a vector?

What is the difference between distance and

displacement?

Distance and displacement are two quantities that might seem the same, but actually have distinct meanings:

Distance: is a scalar quantity of how much ground did an

object cover

Displacement: is a vector quantity of how far out of place (original point) an object is

Scalar is only a measured magnitude

Vector is a measured magnitude + direction

2 What is the difference between speed and

velocity?

How to calculate speed and velocity?

Speed and Velocity are two quantities that might seem the

same, but actually have distinct meanings:

Speed: is the rate of change in distance ( v = d/t)

Velocity is the rate of change in displacement ( d t)

3 What is acceleration?

How to find acceleration from a velocity-time

graph

Acceleration is the rate of change in elocit a t)

Acceleration is the slope of a velocity-time graph

4 What is the relationship between displacement, velocity and acceleration from the graphs?

Velocity is the slope of displacement-time graph, and acceleration is the slope of the velocity-time graph. Velocity

is the area under the acceleration-time graph, and

displacement is the area under the velocity time graph

5 How to solve kinematic problems?

There are 5 equations in kinematics that will be derived. Each

equation has 3 known variables, one unknown variable, and one variable that is not used (there are five variables in total:

Δd, 1, v2, a, & t). Based on the given information from a

problem, students will know which equation to use.

6 What is a free fall?

How does an object in free fall behave when it

is close to earth surface?

What is terminal velocity?

When an object is in free-fall near the earth surface, it

accelerates downwards 9.8 m/s2 due to gravity. This value is

called “g”. In case of air resistance during free-fall, un object

will reach a point of constant speed called “terminal elocit ”

7 What are some of the applications of

kinematics?

Students will use a ticker tape timer to record the motion of

an accelerating toy car. They will create graphs of velocity

and acceleration versus time, and show how these graphs demonstrate constant acceleration.

8 How to calculate vectors in 2-dimenssion?

The understanding of the motion of objects in two

dimensions both conceptually and experimentally. When

completed the students should have an understanding of the vertical and horizontal components and how they relate to

each other. *

9 What is projectile motion?

What factors affect projectile motion?

Students will be introduced to projectile motion through

exploration with various ball-shaped objects. Factors that affect projectile motion will be discussed. **

10

How to analyze projectile motion in 2-

dimenssion?

Continuing discussion on projectile motion. Students will be

introduced to the river gorge supply delivery scenario and brainstorm ways to approach problems. Students will be

introduced to the next class’s experiment**

11 What are some of the applications of projectile

motion? At what initial degree would give the greatest

range?

This laboratory exercise is intended to allow students to

observe and vary the path of a projectile. Students will use a projectile launcher to test the trajectory path of the projectile

motion.

12 What are some of the applications of projectile

motion? At what initial degree would give the greatest

range?

Continuation of Day 11 + Lab report

13 What are real-life applications of kinematics? Students will explore real-life applications of kinematics. E.g.

automotive industry, missiles, free fall, etc.

14 How well prepared are you for the unit test?

Unit test review session. Students will be given sample questions to help them prepare for the unit test. Students may

work in groups. Few questions will be answered as class

discussion

15 How well will you do on the unit test?

Unit test

* www.bemidjistate.edu/academics/departments/science/k12-science-units/2D-motion-unit-HS-physics.pdf

** http://www.ncsec.org/cadre2/team29_2/catapult/Lesson_Plans__Projectile_Motion_to_the_Rescue.html

L HOTS MULTIPLE INTELLIGENCE

1 Knowledge, Comprehension Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal



4 Knowledge, Comprehension, Application, Analysis Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal


6 Comprehension, Application, Analysis Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal

7 Knowledge, Comprehension, Application, Analysis, Synthesis,

Evaluation

Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal




11 Comprehension, Application, Analysis, Synthesis, Evaluation Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal,

Naturalistic

12 Comprehension, Application, Analysis, Synthesis, Evaluation Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal, Naturalistic

http://www.bemidjistate.edu/academics/departments/science/k12-science-units/2D-motion-unit-HS-physics.pdf

http://www.ncsec.org/cadre2/team29_2/catapult/Lesson_Plans__Projectile_Motion_to_the_Rescue.html


14 Knowledge, Comprehension, Application, Analysis, Synthesis Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal

15 Knowledge, Comprehension, Application, Analysis, Synthesis Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal

L KEY RESOURCES (4) PRIOR KNOWLEDGE/LEARNING DIAGNOSTIC ASSESSMENT

1 Text book: Nelson Physics 11

Worksheet

Measurements and IS unites Class exercise (worksheet)


Worksheet

Scalar vs. vector Lesson review at the beginning of class


Worksheet

Displacement, velocity, rate of change Lesson review at the beginning of class


Worksheet

Graph paper

Relationships between displacement,

velocity, and acceleration

Worksheet

5 Text book: Nelson Physics 11 Worksheet

Chart paper

Relationships between displacement, velocity, and acceleration

Small group discussion. Represent relationships on a chart paper


Worksheet

Stopwatch, ticker tape timer, ticker tape, calculator, meter stick, ring stand support, pull-back car

Access to the computer lab

Acceleration and the rate of change of

velocity, gravity

Start class with a small demo involving free

fall. Ask students for their predictions


Worksheet Stopwatch, ticker tape timer, ticker tape, calculator,

meter stick, ring stand support, pull-back car

Kinematic equations

Writing a scientific lab report

Provide clear and thorough instructions

Ask student about key formulae Provide a brief lab demo


Graph paper, rulers

2-dimenssion, vectors and scalars, displacement

Lesson review at the beginning of class


Worksheet Various ball-shaped objects: paper balls, balloon,

cotton balls, rubber balls, tennis balls, golf balls

Kinematic equations

2-dimenssion motion

Class discussion

10

Text book: Nelson Physics 11

Worksheet Projectile launcher and plastic balls

Measuring sticks, Carbon paper and white paper,

Sticky tape, C-clamp

Factors that affect projectile motion from

previous class

Small groups worksheet review


Projectile launcher and plastic balls

Measuring sticks, Carbon paper and white paper, Sticky tape, C-clamp

Projectile motion Provide clear and thorough instructions Ask student about key formulae

Provide a brief lab demo


Worksheet

Projectile launcher and plastic balls Measuring sticks, Carbon paper and white paper,

Sticky tape, C-clamp

Access to the computer lab

Projectile motion

Writing a scientific lab report

None

(Lab day)


Worksheet

Chart paper

Kinematics Lesson review at the beginning of class


Worksheet

Kinematics Class discussion of important concepts in

kinematics

15 Test Papers Kinematics None

(Summative assessment)

L THREE STAGES OF LESSON DEVELOPMENT

1 Review of IS unites and measuring techniques

Worksheet exercise

Some lecturing,

Class discussion and activities on the scalars & vectors, and distance & displacement

Class debriefing

2 Review of previous class

Discuss the concept of speed

Some lecturing,

Class discussion and activities on speed vs.

velocity. How are they calculated? Worksheet

Class debriefing

3 Review of previous class

Ask class what if an object doesn’t mo e in a constant velocity?

Some lecturing,

Class discussion and activities on acceleration. How is it calculated? Worksheet

Class debriefing

4 Review of previous class (worksheet)

Class discussion and activities on the relationships between displacement, velocity,

and acceleration-time graphs

Working on worksheet and graphs

5 Review of previous. Small group discussion.

Represent relationships on a chart paper

Give a simple kinematics problem.

Derivation of the 5 kinematics question Work on an inquiry-based problem

6 Start class with a small demo involving free fall. Ask students for their predictions

Some lecturing, Class discussion and activities on free fall.

How about free fall in other planets?

Work on worksheet Introduction to next class lab experiment

7 Provide clear and thorough instructions

Ask student about key formulae

Provide a brief lab demo

Help students with their experiment and lab report

8 Review of scalars and vectors in 1-D Some lecturing,

Class discussion and activities on calculating vectors in 2-D. Worksheet

Class debriefing

9 Ask students if they know anything about projectile motion?

Discuss applications of projectile motion

Some lecturing, Class discussion and activities on factors

affecting projectile motion

Class debriefing

10 Groups of 4 worksheet review Inquiry-based problem on projectile motion Class debriefing

Introduction to next class lab experiment

11

Provide clear and thorough instructions

Ask student about key formulae Provide a brief lab demo

Help students with their experiment

12 Ask students to spend 5 minutes reviewing what they have done so far from the previous

day and what needs to be done for this lab

Help students with their experiment Help students with their lab report

13 Overall review and ideas of kinematics

applications

Students form groups of 4. Each group has to

come up with a written paragraph on one

application of kinematics. They have to use scientific knowledge learnt

5-minutes presentation/group on kinematics

applications

14 Class discussion of important concepts in

kinematics

Students work on the review sheet Answering few questions on the board

15 Unit Test

L FORMATIVE ASSESSMENT SUMMATIVE ASSESSMENT

1 Class performance and group work None



4 Class performance and group work Hand in worksheet and descriptions on displacement-time, velocity-time, and acceleration-time graphs. The relationships between these

graphs

5 Inquiry-based problem based on kinematics equations Students submit their solution

6 Class discussion and debriefing None

7 Performance during experiment Final lab report


9 Class discussion and debriefing None

10 Inquiry-based problem based on projectile motion Students submit their solution

11 Performance during experiment None

12 Performance during experiment Final lab report

13 Group discussion 5 minutes presentation on applications of kinematics

14 Solving some practice problems on the board None

15 None Summative test

Lesson Plan – Day 9

Title: Intro to projectile motion Subject: Grade 11 Physics Time: 11:00 – 12:15 Strand: Kinematics

Desired Results

Lesson Description

This is the first lesson on Projectile motion. Students will be introduced to projectile motion through exploration with various ball-shaped objects. Factors that affect projectile motion will be discussed.

Ontario Curricular Overall Expectations

B2. investigate, in qualitative and quantitative terms, uniform and non-uniform linear motion, and solve related problems;

B3. demonstrate an understanding of uniform and non-uniform linear motion, in one and two dimensions

Ontario Curricular Specific Expectations

B2.8 use kinematic equations to solve problems related to the horizontal and vertical components of the motion of a projectile

B3.3 describe the characteristics and gi e examples of a projectile’s motion in ertical and horizontal planes

Lesson Goals

- Students develop an appreciation of projectile motion through various methods, and investigate what variables affect the flight path

(various objects, angles ,initial speed, mass, diameter, initial height, with and without air resistance)

- Use reasoning to explain the predictions.

Success Criteria

- Use reasoning to explain the predictions

- Explain common projectile motion terms in their own words

Assessment

Assessment Mode: Teacher and class provide feedback on the ideas that are generated

Materials

Various ball-shaped objects: paper balls, balloon, cotton balls, rubber balls, tennis balls, golf balls

Worksheet

Lesson Format : What Teachers Do/Say This lesson plan was inspired from: http://www.ncsec.org/cadre2/team29_2/catapult/Lesson_Plans__Projectile_Motion_to_the_Rescue.html

Real Time Activities Time

11:00 Introduction

- Draw a trajectory of a projectile motion on the board and ask student if they know anything that

moves in that motion.

- Explore some of projectile motion applications with the students. E.g. Soldiers and weapon,

firefighters, food packets thrown from helicopters

10

11:10 Exploration

- Students will be split into groups of 3 and will be given at least two different types of balls. Each

group should come to consensus on the factors that affect the shape and duration of the flight path of

the balls.

- Teacher should monitor groups, asking guiding questions to encourage brainstorming

30

11:40 Class Discussion

- Lead class discussion of what factors affect projectile motion. Allow different teams to defend their

choices and come to a class consensus on the important factors. Fill out the worksheet.

30

Lesson Reflection: Teacher and Lesson

To be filled after class


Lesson Plan – Day 10

Title: Projectile motion: Inquiry-based problem Subject: Grade 11 Physics Time: 11:00 – 12:15 Strand: Kinematics

Desired Results

Lesson Description

This is the Second lesson on Projectile motion. Students will explore the applications projectile motion through an inquiry-based problem.

Ontario Curricular Overall Expectations

B1. analyse technologies that apply concepts related to kinematics, and assess the technologies’ social and en ironmental impact;

B2. investigate, in qualitative and quantitative terms, uniform and non-uniform linear motion, and solve related problems;

B3. demonstrate an understanding of uniform and non-uniform linear motion, in one and two dimensions

Ontario Curricular Specific Expectations

B1.1 analyse, on the basis of research, a technology that applies concepts related to kinematics

B2.8 use kinematic equations to solve problems related to the horizontal and vertical components of the motion of a projectile

B3.3 describe the characteristics and gi e examples of a projectile’s motion in ertical and horizontal planes

Lesson Goals

- Understand that projectile motion consists of independent horizontal and vertical motions

- Understand that the horizontal and vertical motions take the same amount of time

- Understand that projectiles move horizontally at a constant velocity, and undergo uniform acceleration vertically

- Solve problems related to the horizontal and vertical components of motion of a projectile using kinematic equations (determine the

range, maximum height, and time of flight foe a projectile’s motion)

Success Criteria

- Be able to solve inquiry-based projectile motion problems

Assessment

Assessment Mode: Teacher and class provide feedback on the ideas that are generated.

Teacher will collect students; solution of the problem for marks

Materials

“Projectile Motion Unit Pre-test” worksheet

“Ri er Gorge Scenario” worksheet

Projectile motion lab handout

Projectile launcher and plastic balls

Measuring sticks

Carbon paper and white paper

Sticky tape

C-clamp

Lesson Format : What Teachers Do/Say This lesson plan was inspired from: http://www.ncsec.org/cadre2/team29_2/catapult/Lesson_Plans__Projectile_Motion_to_the_Rescue.html

Real Time Activities Time

11:00 Introduction

- Ask students to form groups of 4

- Had out the worksheet (see attachment: Projectile Motion Unit Pre-test) and ask groups to work on it

- Discuss the worksheet with the class

20

11:20 Exploration

- Introduce scenario to students and brainstorm ways to approach the River Gorge supply delivery (see 40


attachment).

- Students may work on the problem alone or groups of two.

- Collect students’ work at the end of the work session.

12:00 Conclusion: introducing next class experiment – Teacher’s Demo

- Teacher uses Projectile launcher and plastic balls (and other materials listed) to introduce students to

the experiment they will explore next class

- Distribute lab handout to give students a head start of what to expect

10

Lesson Reflection: Teacher and Lesson

To be filled after class

Projectile Motion Unit Pre-test

This activity is meant to test your prior knowledge going into our chapter on projectile motion. Please do the best that you can, but do not be

discouraged if you don’t know the answers! You will not be graded on this activity. Based on the class’ answers, we will tailor our learning to

ensure everyone will be challenged but not overwhelmed.

1) What force causes an object to fall to the ground when dropped?

Gravity

2) Does a ball dropped out of the window of a moving car take longer to reach the ground than one dropped at the same height from a car at

rest? Why or why not?

No, both balls reach the ground at the same time. This is because motion in the horizontal and vertical directions are independent of one another.

Thus, the fact that the ball dropped from the moving car has a horizontal velocity does not affect the amount of time it take for it to hit the ground.

3) Does the angle of take-off matter to a long jumper? Why?

Yes, the angle will affect how far the long jumper will travel. Using our equation for displacement in the x-direction we see that the distance

depends on the cosine of the launch angle.

4) What is velocity?

Velocity is equal to the change in distance divided by the change in time.

5) Can you find the cosine of 80°?

Cos(80 degrees)=0.7648

6) A soccer ball is kicked at an angle of 20 degrees at 15 m/s and lands 2.5 s later. Determine the distance the ball travels along the ground.

Given: Angle (θ) 20 degrees

Initial Velocity (vi) =15 m/s

Time of Flight (t) =2.5 s

Find: distance traveled in x-direction

Equation: Δx i*cos θ)*t

Δx 36.96 m or 37 m

River Gorge Scenario

You are 6 days into a 2 week hiking trip with a group of friends near the Royal Gorge in Colorado. As you walk along the trail you notice

how steep the cliff walls are that drop down into the Gorge. You and your friends are trying to decide how deep the gorge is (about 365 m)

when you hear cries for help coming from across the Gorge. You notice a group of hikers who appear to be stranded across the river.

They decided to cross the Gorge on a rickety old bridge that gave way just as their last group member finished crossing. The hikers indicate

to you that they have been stranded for 4 days now without any food or water. They are dehydrated and weak; you must do something to

help them! You all try your cell phones but you have no signal. Two of your group members volunteer to hike back out of the wilderness to

alert the authorities, but you know that you must do something to help the hikers until someone can come rescue them. But how will you get

food and water across the Gorge to them? The cliff walls are too steep to climb down. Can you think of any way to help them?

http://personal.udri.udayton.edu/klosterm/Colorado/Hbridge11.jpg

UNIT TEST Taken from: http://webcache.googleusercontent.com/search?q=cache:MfG-lQdvAbYJ:pplazekgrade11physics.wikispaces.com/file/view/SPH3U%2B-

%2BKinematics%2BUnit%2BTest%2Bwith%2Bsolutions.docx+&cd=1&hl=en&ct=clnk&gl=ca

COURSE: PHYSICS, GRADE 11 COURSE CODE: SPH3U

University Preparation

UNIT : KINEMATICS Maximum Marks: 50

Time allotted: 75 minutes

General Instructions:

All Questions are compulsory.

Question No. 1 contains 7 multiple choice questions of 1 mark each.

Question No. 2 contains 5 True-False type questions of 1 mark each.

Question No. 3 to 6 are short answer questions of 2 marks each.

Question No. 7 & 8 are problem solving questions of 10 marks each.

Question No. 9 is long answer question of 10 marks.

Q 1 Following are the multiple choice questions. Tick out the correct answer. (K/U)

1. The term “uniform motion” means a. acceleration is constant d. displacement is constant b. speed is constant e. velocity is zero c. velocity is constant

2. The area under a velocity-time graph always represents a. Displacement d. acceleration b. change in velocity e. change in acceleration c. distance

http://webcache.googleusercontent.com/search?q=cache:MfG-lQdvAbYJ:pplazekgrade11physics.wikispaces.com/file/view/SPH3U%2B-%2BKinematics%2BUnit%2BTest%2Bwith%2Bsolutions.docx+&cd=1&hl=en&ct=clnk&gl=ca

http://webcache.googleusercontent.com/search?q=cache:MfG-lQdvAbYJ:pplazekgrade11physics.wikispaces.com/file/view/SPH3U%2B-%2BKinematics%2BUnit%2BTest%2Bwith%2Bsolutions.docx+&cd=1&hl=en&ct=clnk&gl=ca

3. The position time graph pictured below represents the motions of two objects, A and B. Which of the following statements concerning the objects’ motion is true?

a. Object B travels the greater distance

b. Object A has the greater speed

c. Object A leaves the reference point at the earlier time

d. Both of the objects have the same speed at the point where the lines cross.

e. Object A is travelling for a longer period of time

4. The distance travelled by a body is directly proportional to the square of the time taken. It’s acceleration

a. Increases c. becomes zero

b. Decreases d. remains constant

5. A ball is thrown vertically into the air and when it returns after an interval of 2 seconds, it is caught. Which one of the following statements is true if the acceleration due to gravity is 10 m/s2 and air resistance can be neglected: a. The acceleration at the top of its flight is 10 m/s2. b. The time taken for the descending motion does not equal the time taken for the ascending motion. c. The maximum height it reaches does not depend on the force of gravity. d. The acceleration after it leaves the hand is 10 m/s2 downwards.

d

A

B

t

Position vs Time

6. A rock is thrown vertically upwards with a speed 'v' from the edge of a cliff. At the same moment, a second rock is thrown vertically downwards with the same initial speed 'v'. Which of the following statements regarding the motion of the rocks is true (ignore air resistance.)? a) The rock which was thrown upwards reaches the bottom of the cliff with a higher velocity. b) The rock which was thrown downwards reaches the bottom of the cliff with a higher velocity. c) Both rocks reach the bottom of the cliff with the same velocity at the same time. d) Both rocks reach the bottom of the cliff with the same velocity but at different times.

7.

The path PQR of a soccer ball kicked

from a point P on the ground is shown

in the diagram at the right. At point Q,

the ball is at its maximum height.

Which ONE of the following vectors may represent the acceleration due to gravity of the ball at point Q?

a) A b) B

c) C d) D

Q 2. State TRUE or FALSE for the following statements: (K/U & C)

1. A very massive object will free fall at the same rate of acceleration as a less massive object.

2. An object which is slowing down is represented by a line on a velocity-time graph which is moving in the downward direction.

3. An object with a positive acceleration will be represented on a position-time graph by a line which curves upwards.

4. The direction of the acceleration vector is dependent upon two factors: the direction the object is moving and whether the object is speeding up or slowing down.

5. Person X moves from location A to location B in 5 seconds. Person Y moves between the same two locations in 10 seconds. Person Y is moving with twice the speed as person X.

Q 3. A train of 150m length is going towards north direction at a speed of 10 m/s. A parrot flies at a speed of 5m/s towards south direction parallel to the

railway track, find the time taken by the parrot to cross the train? (K/U)

Q 4. The direction in which an object moves is given by the direction of velocity of the object and not by the direction of acceleration. Explain the

statement with suitable example. (A & C)

Q 5. In long jump, does it matter how high you jump? What factors determine the span of the jump?

(K/U & C)

Q 6. There are two displacement vectors, one of magnitude 3 meters and the other of 4 meters, how would the two vectors be added so that the

magnitude of the resultant vector be (a) 7 meters (b) 1 meters? (K/U)

Q 7. A shell was fired from ground level with an initial speed of 3.5 x 102 m/s at an angle of 30o to the horizontal. Estimate:

(K/U)

i its time of flight;

ii its maximum altitude

iii its range

Q 8. Two sport cars start from rest at the same place. One accelerates at 0.90 ms-2 for 15 s, and continues at constant speed there after. The other accelerates at 0.85 ms-2 for 20 s and then remains at that speed. Draw both journeys on the same velocity-time graph and determine the time and distance that the second car overtakes the first car. (K/U)

Q 9. When a skydiver jumps from an airplane she can reach speeds near 140 km/h during the freefall portion of the dive. Once the parachute is

deployed the parachutist’s speed decreases to 10 km/h. Explain why then in physics we consider the acceleration during the freefall to be

negative and the acceleration during the time the parachute is deployed to be positive by using your knowledge of vectors and kinematics. (A)

SOLUTIONS

Q 1. 1. c

2. a

3. b

4. d

5. d

6. d

7. c

Q 2. 1. True

2. False

3. False

4. True

5. False

Q 3. Relative velocity of Parrot with respect to train = 5+10 = 15m/s

Time taken by parrot to cross the train, t = 150/15 = 10s

Q 4. When an object is thrown up, the direction of motion of the object and hence its velocity is along vertical in upward direction. As the object moves

up, it is always attracted by earth in downward direction i.e., the acceleration is in vertical downward direction. Hence the direction of motion of the

object is that of velocity and not that of acceleration.

Q 5. Yes, in long jump, it matters how high one jumps, it is explained below.

For initial velocity u and angle of projection ϴ the maximum height,

h = u2 Sin2ϴ or u2 = 2 h

2g g Sin2ϴ

and, horizontal range, R = u2 Sin 2 ϴ = 2 h 2Sin ϴ Cos ϴ = 4h Cot ϴ

g Sin2ϴ

Thus the span of jump depends upon (i) height h attained (ii) angle of projection, ϴ.

Q 6. The magnitude of resultant R of two vectors A and B is given by

R = √ A2+B2+ 2 AB Cos ϴ ; where A=3m and B=4m

Now R = √ 32+42+ 2×3×4 Cos ϴ .

(i) R will be 7m if ϴ = 0o

(ii) R will be 1m if ϴ = 180o

Q 7. Take up as positive.

Initial horizontal speed = 3.5 x 102 m/s cos 30o

= 3.0 x 102 m/s

Initial vertical speed = 3.5 x 102 m/s sin 30o

= 175 m/s

Vertical Motion to top of flight:

v1 = +175 m/s

v2 = 0

a = -9.81 m/s2

t = [v2 - v1]/t = 17.8 s

So, time of flight = 2 x 17.8 s = 36 s

vav = [175 m/s + 0]/2 = 87.5 m/s

So, y = vav t = 87.5 m/s x 17.8 s = 1.6 x 103 m

Horizontal Motion:

x = vx t = 3.0 x 102 m/s x 36 s = 1.1 x 104 m

Q 8.

The velocities they reach are 0.9 × 15 = 13.5 ms-1 and 0.85 × 20 = 17 ms-1 respectively. Similar to the problem above, we have: First car (red) distance at time t = 1/2 × 13.5 (t + t - 15) Second car (blue) distance at time t = 1/2 × 17 (t + t - 20) The distance when they meet is the same, so: 1/2 × 13.5 × (2t - 15) = 1/2 × 17 × (2t - 20) Solving gives: Time = 19.643 s

Distance = 163.93 m

Q 9. Since the skydiver jumps from a plane the acceleration due to gravity causes the divers speed to increase in the negative direction. Therefore the

diver’s velocity continues to become more negative over time. If the diver is traveling at a speed of 140km/h, his/her velocity would be -140km/h or

140km/h [D]. Once he/she pulls deploys the parachute, the speed begins to decrease meaning that the velocity is becoming less negative. i.e. changing

from -140km/h to -10km/h. Therefore from a vector perspective the change in velocity is positive

∆v = v2 – v1

= (-10) – (-140) = +130 m/s

Since the velocity changes positive, therefore the acceleration must be positive.

i.e. a = ∆ v / ∆ t

unit plan - grade 11 u...

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