Transcript Projectile Motion - Solon City Schools

Projectile Motion
Type I
Type II
Projectile 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
(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:
zzzzzzzzzzzzzzzzzzzz
1.
2.
3.
4.
What do you notice about the arrows representing the downward
velocity? (dropped)
What do you notice about the arrows representing the vertical
velocities? (fired) the horizontal arrows?
How do downward velocities compare? (dropped vs. fired)
Which hits first?
Type I Projectile Motion Analysis
Type I Animation
(watch magnitude of velocity arrows)
Type I Projectile Motion Analysis
Equations
“X” direction
dx = vx x t
vx = dx / t
“Y” direction
dy = ½ gt2
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)
◦ Vfy at top = 0.0 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 (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