Projectile MotionProjectile Motion

The Path of a ProjectileThe Path of a Projectile

An object thrown off a cliffA basketball free throwA golf shotA cannon ball

Trajectory

The path (trajectory)of a projectile is a parabola

Parabolic motion of a projectile

Horizontal and vertical motion are independent (90°)

There are the two components of the projectile's velocity – horizontal vX and vertical vY .

The horizontal component of it’s velocity does not change.

vX is constant

Gravity is the only force

Horizontal and vertical motion are independent!

Describe the Trajectory…Describe the Trajectory…

The projectile will move along it’s path in both the horizontal (x) direction and the vertical (y) direction at the same time.

The two directions are independent of each other.

Example

1. A rock is thrown horizontally from a high cliff at 40 m/s.

What is the horizontal component of its velocity 3 seconds later?

. A rock is thrown horizontally from a high cliff at 40 m/s.

What is the vertical component of its velocity 3 seconds later?

. A rock is thrown horizontally from a high cliff at 40 m/s.

What is the magnitude of the velocity vector 3 seconds later?

. A rock is thrown horizontally from a high cliff at 40 m/s.

What is the direction of the velocity vector 3 seconds later?

homework

Review Book: Read pg 39-41 Text Book: Read pg 146 - 150 Do problems 1-3 on page 150 in text

Do Now

An object is thrown outward from a cliff with a horizontal velocity of 20m/s. Object takes 15 s to reach the bottom of the cliff (ignore air resistance). Calculate:

1.The height of the cliff

2.The horizontal distance traveled by the object by the time it reaches the ground

Determining the HeightDetermining the Height

You can determine the height at any point in the trajectory!

2

2

1attvy y

What is acceleration?What is acceleration?

In the y direction a is always the acceleration of gravity, g.

Therefore,

2

2

1gttvy y

Horizontal velocity is 20m/s. Object takes 15 s to reach the

bottom of the cliff 1. The height of the cliff

) m 1100 (i.e., 5.1102

)15)(/8.9(2

10

2

1

22

2

downwardmy

ssmy

gttvy y

Determining the RangeDetermining the Range

You can determine the displacement (range) of a projectile any any point

along the trajectory.

tvx x

Horizontal velocity is 20m/s. Object takes 15 s to reach the

bottom of the cliff 2. The horizontal distance traveled by the

object by the time it reaches the ground

mssmx

tvx x

300)15)(/.20(

Consider an object such as a cannonball that is fired at an

angle to the ground If the initial velocity of

the object is vi and the angle is θ, we must resolve the x- and y- components.

v

sin

cos

iiy

ii

vv

vv x

vX is constant vy changes

Some Other Important NotesSome Other Important Notes

At the highest point of the trajectory, it is the exact midpoint of the time.

It takes the projectile half of the time to get to the top.

Still More NotesStill More Notes

When the projectile gets to the top, it has to stop going up and start going down.

Therefore, the velocity in the y-direction at the highest point is zero for a split second.

and Still More Notesand Still More Notes

As the projectile starts to fall down, it is simply in free fall.

The velocity in the x-direction remains constant throughout the entire trajectory.

Trajectory and Range Maximum range

is at 45° Low and high

trajectory cover the same distance.

30 and 60 10 and 80 25 and…

Component of Motion

Equation

X Acceleration                    

Y Acceleration                        

X Velocity                               

Y Velocity                                            

X Position                                      

Y Position

                                            

    

Homework

Test Corrections Review book pg 41-42 # 74 -86 Show all

work

Example: A ball is thrown with an initial velocity of 25 m/s at 40º to the horizontal.

1. What is vx at the highest point?

19 m/s

2.  What is vy at the highest point?

 0 m/s

smv

smv

iy

ix

/1640sin25

/1940cos25

A ball is thrown with an initial velocity of

25 m/s at 40º to the horizontal.3. What is the speed at the highest point?

19 m/s

4. How long does it take the ball to get to its highest point?

st

t

gtvv yy if

6.18.9/16

)8.9(160

Example 2

Courtney kicks a soccer ball @ rest on level ground giving it an initial velocity of 7.8 m/s @ an angle of 32 degrees.

a)How long will the ball be in the air?

b)How high will the ball go?

c)What will be its range?

Let’s Try another Problem!Let’s Try another Problem!

A stone is thrown horizontally at a speed of 5.0 m/s from the top of a cliff 78.4 m high

1. How long does it take the stone to reach the bottom of the cliff?

Problem continued…Problem continued…

2. How far from the base of the cliff does the stone strike the ground?

3. What are the horizontal and vertical components of the velocity of the stone just before it hits the ground?

and Another Problem…and Another Problem…

A steel ball rolls with a constant velocity on a tabletop 0.950 m high. It rolls off and hits the ground 0.352 m from the edge of the table. How fast was the ball rolling?