Projectile Motion

If you throw a javelin…

What affects it’s flight?– Gravity– How hard you throw it (initial velocity)– What angle you throw it at– Air resistance (shape of javelin)– Mass

Which one of these has no affect?

Let’s take a look at how they affect flight!

http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/ProjectileMotion/jarapplet.html

We call the arc of the javelin toss: Projectile Motion

• Projectiles travel along a curved trajectory

Projectile Motion

• A video introduction

What is a Projectile?• Projectile

– an object that moves along a 2-D curved trajectory

- does not have any propulsion when in flight

• Examples: – Football, baseball, tennis ball, etc–Bullets– Snow boarders in a half pipe–Cliff divers

Projectile Motion Example # 1

What do you notice about these two projectiles?

Did you notice?• The projectiles hit the ground at the same

time regardless of horizontal velocity• Object accelerates downwards (at 9.81 m/s2 –

acceleration due to gravity)• Horizontal displacement stays constant

throughout motion

Conclusions about Projectile motion

1) The horizontal component of a projectile’s velocity is constant (no acceleration)

2) Projectile experiences constant downwards acceleration (gravity)

3) Horizontal and vertical motion of a projectile are independent of each other (except they have a common time)

Projectile Motion Example # 2

Important Variables

• Time – Δt• Velocity – v• Height – Δdy

• Distance – ΔdX

• Acceleration – a• Launch Angle - θ

Strategy to Solving Projectile Motion Problems

• Analyze horizontal motion and vertical motion independently–Separate the velocity vector into x-

and y- components• Remember: Time is common

between them

Horizontal motion:- Constant velocity (0 accel.) in the x direction- Equation : v = d/t

Vertical motion:- Constant acceleration - 9.8 m/s2

[down]- Use the accel. equations we used previously

Two Types of Problems: One Dimensional Problems (no horiz. Velocity)

Case 1: Object dropped from restCase 2: Object thrown directly upwards

Two Dimensional Problems:Case 3: Rolled over an edgeCase 4: Shot at an angle

Let’s analyze the four cases!

For Two Dimensional Problems:

Break the initial velocity into horizontal and vertical components (using the given angle and trigonometry)

vy

θ

vx

Projectile Motion Example # 3

Example Question (Case 3)A tennis ball is rolled off a counter at 8 m/s,

what will it’s position be after 3s?

Example Question (Case 4)A golfer strikes a golf ball on level ground. The

ball leaves the ground with an initial velocity of 42 m/s [32o above the horizontal].

a) What will the ball’s position be after 4 s?b) What will be the maximum height attained?