Projectile MotionProjectile Motion

Type I Type II

Projectile MotionProjectile Motion

•Any object that has been given an initial force, 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 simultaneously (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

Projectile Motion Projectile Motion (X & Y motion is (X & Y motion is independent)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 verticalmotion.

Type I Projectile Motion Type I Projectile Motion AnalysisAnalysisA cannon ball is fired at the exact time

another cannon ball is dropped:

1. What do you notice about the arrows representing the downward velocity? (dropped)

2. What do you notice about the arrows representing the vertical velocities? (fired) the horizontal arrows?

3. How do downward velocities compare? (dropped vs. fired)

4. Which hits first?

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Type I Projectile Motion Type I Projectile Motion AnalysisAnalysis

Type I Animation(watch magnitude of velocity

arrows)

Type I Projectile Motion Type I Projectile Motion AnalysisAnalysis

Equations“X” direction “Y”

directiondx = vx x t dy = ½ gt2

vx = dx / t vfy = g x t

Proof that motion is independent

Type II Projectile Motion Type II Projectile Motion AnalysisAnalysis

Steps to solving type II problems:◦Vix = Vi Cos

◦Viy = Vi Sin

Type II Projectile Motion Type II Projectile Motion AnalysisAnalysisType II Facts:

◦Perfect symmetry (time up = time down; Vi = Vf Vix = Vfx & Viy = - Vfy ; Vx = constant)

◦Vfy at top = 0.0 m/s

◦Hang time = total time in air◦Time to max height = ½ hang time

Type II Projectile Motion Type II Projectile Motion AnalysisAnalysisType II Equations:

◦dx = Vix x t (range; use hang time)

◦Vfy = Viy + gt (used for time to max ht.)

◦dy = Viyt + ½ gt2 max ht. (use time to max ht.)

◦Hang Time = Time to max ht. x 2