Projectile Motion

1. Projectile Motion Type I Type II

2. Projectile Motion Any object that has been given an initial thrust, then moves only under the force of gravity. The path of a projectile is called the trajectory The motion of the object is in two directions (1st time) To solve projectile motion problems, solve all variables individually The motion of a projectile in the “X” direction is independent of the motion in the “Y” direction

3. Projectile Motion (X & Y motion is independent) • Still shots of two golf balls falling. • Red ball has “0” initial velocity (free fall) • Yellow ball has initial “X direction” velocity (type I projectile) • Notice horizontal motion doesn’t effect vertical motion.

4. Type I Projectile Motion Analysis • A cannon ball is fired at the exact time another cannon ball is dropped: • What do you notice about downward velocity? (dropped) • What do you notice about velocities of the fired cannon ball? • How do downward velocities compare? • Which hits first? zzzzzzzzzzzzzzzzzzzz

5. Type I Projectile Motion Analysis Type I Animation (watch magnitude of velocity arrows)

6. Type I Projectile Motion Analysis Equations “X” direction“Y” direction dx = vx x t dy = ½ gt2 vx = dx / t vfy = g x t Proof that motion is independent

7. Type II Projectile Motion Analysis • Steps to solving type II problems: • Vix = Vi Cos • Viy = Vi Sin

8. Type II Projectile Motion Analysis • Type II Facts: • Perfect symmetry (time up = time down; Vi = Vf Vix = Vfx & Viy = - Vfy ; Vx = constant) • Vy at top = 0 m/s • Hang time = total time in air • Time to max height = ½ hang time

9. Type II Projectile Motion Analysis • Type II Equations: • dx = Vix x t (also used for hang time) • Vfy = Viy + gt (also used for time to max ht.) • dy = Viyt + ½ gt2 max ht.(use ½ time) • Hang Time = Time to max ht. x 2