# Projectile Motion - PowerPoint PPT Presentation

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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

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Projectile Motion

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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

### 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:

• 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 Projectile Motion Analysis

Type I Animation

(watch magnitude of velocity arrows)

### 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

### Type II Projectile Motion Analysis

• Steps to solving type II problems:

• Vix = Vi Cos

• Viy = Vi Sin

### 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

### 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