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

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Projectile Motion

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Projectile motion

Projectile Motion

Type I Type II


Projectile motion1

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

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

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


Type i projectile motion analysis1

Type I Projectile Motion Analysis

Type I Animation

(watch magnitude of velocity arrows)


Type i projectile motion analysis2

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

Type II Projectile Motion Analysis

  • Steps to solving type II problems:

    • Vix = Vi Cos

    • Viy = Vi Sin


Type ii projectile motion analysis1

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 analysis2

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


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