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Projectile Motion

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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 (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

- 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.

- 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?

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Type I Animation

(watch magnitude of velocity arrows)

Equations

“X” direction“Y” direction

dx = vx x t dy = ½ gt2

vx = dx / t vfy = g x t

Proof that motion is independent

- Steps to solving type II problems:
- Vix = Vi Cos
- Viy = Vi Sin

- 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

- 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