Projectiles

Horizontally Shot Projectiles Objects launched or shot are called projectiles. Their path is curved and called a trajectory. Gravity causes the object to fall vertically, so vy constantly changes.

The projectile moves horizontally because of inertia. If you ignore air resistance, the horizontal velocity is constant; vx is constant. vx

vx vxy vy The horizontal and vertical velocities are independent. Together they cause the path of the projectile to be curved : parabolic. hlp.gif vx vxy vy

bds.gif

An object dropped at the same time another is shot horizontally will hit the ground at the same time. Only gravity causes it to fall down. Assume no air resistance

If your reference is moving with the projectile, the projectile appears to fall straight down. pap.gif

vy0 for horizontal motion is zero! vx vyi=0 (Draw) y x x = vxt y = vy0t + ½ at2 vy0 for horizontal motion is zero!

Projectiles shot at an Angle! You are giving the object an initial velocity, vi

This velocity has two components, vx and vy Vx = v0cosθ Vy0 = v0sinθ tb.gif

vy = 0, vx (Draw) ymax ½t v0 vy0  vx Range, x Total time t

The final vertical velocity is equal to the initial vertical velocity but opposite in direction. The horizontal velocity, vx, is constant. Assume air resistance = 0

Rising time = falling time Distance up = distance down Y = 0 at the start (t = 0) and the end (t = total) Max height, ymax happens at midpoint, ymax at ½ total time.

mr.gif Maximum range is at 45° sin45° = cos45° ; vx = vy0 Angles more than 45° have a longer hang time. Angles less than 45° have a shorter hang time.

So you want to know about “Monkey Gun?” You are a zoo keeper and want to shoot bananas up to the monkey. The monkey gets scared when it hears the cannon and lets go and falls to the ground. What if there is no gravity? mzng.gif What happens when you aim above the monkey? mzg.gif What if you shoot the banana slow? mzs.gif What if you shoot the banana fast? mzf.gif

Example Problems Homework – Projectile Motion