Projectile Motion What is a Projectile Projectile an

Projectile Motion

What is a Projectile? • Projectile – an object that moves along a 2 -D curved trajectory - does not have any propulsion when in flight

Yes Examples • • Tennis ball Football Golf ball Basketball Javelin Jumping out of a car Cannon ball Non Examples • Plane • Rocket • Missile

Projectile Motion Example # 1

The ball is in free fall vertically and moves at constant speed horizontally!!!

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 – vi, vf Height – Δdy Distance – Δd. X Acceleration – a Launch Angle - θ

Strategy to Solving Projectile Motion Problems • Analyze horizontal motion and vertical motion independently –Separate the velocity vector into xand y- components • Remember: Time is common between them • Use an x/y chart to list givens

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

Vertical motion: - Constant acceleration - 9. 81 m/s 2 [down] - Use the accel. equations we derived

Two Types of Problems: One Dimensional Problems (no horiz. Velocity) Case 1: Object dropped from rest Case 2: Object thrown directly upwards Two Dimensional Problems: Case 3: Rolled over an edge Case 4: Shot at an angle

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 1 A tennis ball is rolled off a counter at 8 m/s, what will it’s position be after 3 s? Example Question 2 A golfer strikes a golf ball on level ground. The ball leaves the ground with an initial velocity of 42 m/s [32 o above the horizontal]. a) What will the ball’s position be after 4 s? b) What will be the maximum height attained?

• Example # 3: A cannonball is fired with velocity of 50. 0 m/s [30º above the horizontal]. It is shot at the level battle field which is located 20. 0 m below. • a) Calculate the horizontal displacement of the cannonball. • b) Calculate the impact velocity of the cannonball