Projectile Motion
Things don’t always move in a straight line. When an object moves in two dimensions, we look at vector
components.
The super-duper-important general rule is this: An object’s motion in one dimension does not affect
its motion in any other dimension .
The most common kind of two-dimensional motion you will encounter is projectile motion. The
typical form of projectile-motion problems is the following:
“A ball is shot at a velocity v from a cannon pointed at an angle è above the horizontal ...”No matter what the problem looks like, remember these rules:
• The vertical component of velocity, vy , equals v (sin θ ).
• The horizontal component of velocity, vx , equals v (cos θ ) when θ is measured relative to the
horizontal.
• Horizontal velocity is constant.
• Vertical acceleration is g , directed downward.
Here’s a problem that combines all of these rules:
A ball is shot at a velocity 25 m/s from a cannon pointed at an angle θ = 30° above the horizontal. How
far does it travel before hitting the level ground?We begin by defining “up” to be positive and writing our tables of variables, one for horizontal motion
and one for vertical motion.