Projectile Motion Type I Type II

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 (1 st 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

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.

Type I Projectile Motion Analysis A cannon ball is fired at the exact time another cannon ball is dropped: 1. What do you notice about downward velocity? (dropped) 2. What do you notice about velocities of the fired cannon ball? 3. How do downward velocities compare? 4. Which hits first? zzzzzzzzzzzzzzzzzzzz

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

Type I Projectile Motion Analysis Equations “X” direction “Y” direction d x = v x x t d y = ½ gt 2 v x = d x / t v fy = g x t Proof that motion is independent

Type II Projectile Motion Analysis Steps to solving type II problems: ◦ V ix = V i Cos ◦ V iy = V i Sin

Type II Projectile Motion Analysis Type II Facts: ◦ Perfect symmetry (time up = time down; V i = V f  V ix = V fx & V iy = - V fy ; V x = constant) ◦ V y at top = 0 m/s ◦ Hang time = total time in air ◦ Time to max height = ½ hang time

Type II Projectile Motion Analysis Type II Equations: ◦ d x = V ix x t (also used for hang time) ◦ V fy = V iy + gt (also used for time to max ht.) ◦ d y = V iy t + ½ gt 2  max ht. (use ½ time) ◦ Hang Time = Time to max ht. x 2