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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 Non Examples
• Tennis ball• Football• Golf ball• Basketball• Javelin• Jumping out of a car• Cannon ball
• 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 – 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• 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/s2 [down]- Use the accel. equations we
derived
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
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 1A tennis ball is rolled off a counter at 8 m/s,
what will it’s position be after 3s?
Example Question 2A 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?
• 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