2 Dimensional 2 Dimensional motionmotion

Relativity of VelocityRelativity of VelocityTheory, developed in the early 20th Theory, developed in the early 20th century, which originally attempted to century, which originally attempted to account for certain anomalies in the account for certain anomalies in the concept of relative motion, but which in its concept of relative motion, but which in its ramifications has developed into one of ramifications has developed into one of the most important basic concepts in the most important basic concepts in physical science physical science Velocity changes when compared to a Velocity changes when compared to a frame of reference frame of reference Velocity can broken down into 2 Velocity can broken down into 2 dimensions.dimensions.– The vertical (free-fall acceleration)The vertical (free-fall acceleration)– The horizontal (constant velocity)The horizontal (constant velocity)

Types of AccelerationTypes of Acceleration

AccelerationAcceleration , also known as linear , also known as linear acceleration, rate at which the velocity acceleration, rate at which the velocity of an object changes per unit of time. of an object changes per unit of time. A = A = v/t (v/t (Average Acceleration)Average Acceleration)

Uniform AccelerationUniform Acceleration : the constant : the constant rate of change in Velocity ( Free Fall )rate of change in Velocity ( Free Fall )– 9.81 m/s9.81 m/s2 2 (use 10 m/s(use 10 m/s2 2 in multiple choice)in multiple choice)

Vertical And Horizontal Vertical And Horizontal ComponentsComponents

Horizontal and Vertical components of motion are independent.

A Cannon is fired Horizontally from cliff

View this from two reference frames:

1.Reference frame moving across.

2.Reference frame on the ground.

Vertical and Horizontal Vertical and Horizontal Components #2Components #2

the ball follows a parabolic the ball follows a parabolic path and remains directly path and remains directly above the launcher at all above the launcher at all timestimes

As the ball rises towards its As the ball rises towards its peak, it undergoes a peak, it undergoes a downward accelerationdownward acceleration

In the absence of horizontal In the absence of horizontal forces, there would be a forces, there would be a constant velocity in the constant velocity in the horizontal direction horizontal direction

A ball is projected straight upwards by a A ball is projected straight upwards by a launcher located in the bed of the trucklauncher located in the bed of the truck

Vertical and Horizontal Vertical and Horizontal Components #3Components #3

The banana moves in a The banana moves in a parabolic path in the parabolic path in the presence of gravitypresence of gravity

The monkey also The monkey also accelerates downward accelerates downward once he lets go of the limb.once he lets go of the limb.

Both banana and monkey Both banana and monkey experience the same experience the same acceleration since gravity acceleration since gravity causes all objects to causes all objects to accelerate at the same accelerate at the same rate regardless of their rate regardless of their massmass

The Monkey and Zookeeper feeding with a cannon

FormulasFormulas

How to choose the best formulaHow to choose the best formula•Free Fall

•Acceleration due to gravity

•Uniform acceleration

•Distance is not part of the question

•Time is part of the question

How to choose the best formulaHow to choose the best formula

•Free Fall•Acceleration due to gravity•Uniform acceleration•Distance is part of the question•Time is part of the question

How to choose the best formulaHow to choose the best formula

Choose this formula when the question does not include the TIME

Sample Problem #1Sample Problem #1

A brick falls freely from a high A brick falls freely from a high scaffold at a construction site.scaffold at a construction site.

What is the velocity after 4 seconds?What is the velocity after 4 seconds? How far does the brick fall in this time?How far does the brick fall in this time?

Solution Solution Given: a = 10 m/sGiven: a = 10 m/s2 2 t = 4s t = 4s

Vf = 0 m/s + (-10.0 m/s2) ( 4.0 s)

= -40 m/s

d = 0 m/s (4s) + .5(-10.0 m/s2) (4s)2

= 0 + .5(-10.0m/s2) (16 s2 )

= -80m

What is the velocity What is the velocity after 4 seconds? Find: Vafter 4 seconds? Find: V

How far does the How far does the brick fall in this brick fall in this time? Find: dtime? Find: d

Sample problem #2Sample problem #2

An airplane must reach a speed of An airplane must reach a speed of 71m/s for takeoff. If the runway is 71m/s for takeoff. If the runway is 1000m long, what must be the 1000m long, what must be the acceleration?acceleration?

SolutionSolution

(71m/s)2 = (0 m/s)2 + 2 (a) ( 1000m)

(-2000m) a = - 5041 m2 / s2

What is the acceleration needed to What is the acceleration needed to take off?take off?

Given: Vi=0 m/s Find: a =?

Vf=71 m/s d=1000m

a = 2.5 m/s 2

Sample Problem #3Sample Problem #3

Melanie rolls a .010 kg Melanie rolls a .010 kg marble down a ramp marble down a ramp and off the table with and off the table with a horizontal velocity of a horizontal velocity of 1.2 m/s. The marble 1.2 m/s. The marble falls into a cup placed falls into a cup placed 0.51 m from the 0.51 m from the table’s edge.table’s edge.

How high is the table?How high is the table?

Solution to Problem #3 part 1Solution to Problem #3 part 1

Given: dGiven: dxx=0.51m V=0.51m Vxx=1.2 m/s=1.2 m/s

Find: dFind: dyy=?=?

Need to find t=?Need to find t=?

Formula v=d/tFormula v=d/t

1.2 m/s = 0.51m/t1.2 m/s = 0.51m/t

t = 0.51m / 1.2 m/st = 0.51m / 1.2 m/s

t = 0.43 st = 0.43 s

Solution to Problem #3 part 2Solution to Problem #3 part 2

Given: dGiven: dxx=0.51m V=0.51m Vxx=1.2 m/s=1.2 m/s

Find: dFind: dyy=?=?

Found t=.43sFound t=.43s

Formula dFormula dyy= 1/2 g t= 1/2 g t22

ddyy= 1/2 (10m/s= 1/2 (10m/s22) (0.43s)) (0.43s)22

ddyy= (5m/s= (5m/s22) (0.1849)) (0.1849)

ddyy= 0.92 m= 0.92 m

SummarySummary

Determine the type of motionDetermine the type of motion

List the given informationList the given information

Choose the best formula from the Choose the best formula from the Physics formulasPhysics formulas

Substitute the proper unitsSubstitute the proper units

Solve for the unknown in the Solve for the unknown in the equationequation