Session 5 - Projectile Motion

Projectile motion is a beautiful, but slightly tricky application of vectors. It's vector math mixed with one-dimensional motion.

First, let us consider vector components. Just like 2 vectors can be added together to give a resultant vector, a single vector can be "deconstructed" into its "perpendicular components."

If the angle is measured with respect to horizontal, a vector V at angle theta (T) has components:

Vh = V cos (T)

Vv = V sin (T)

Horizontal (h)

Vertical (v)

And now, projectiles:

Consider first a projectile launched with nothing but horizontal velocity (vox), from a vertical height (xy). There is NO horizontal acceleration, ONLY vertical acceleration. So, the ball lands in the same exact time as if it had been simply dropped. True, it goes further horizontally, but it doesn't take any longer to do that. This will be demonstrated in class.

To solve projectile motion problems, you still use equations of motion, but you use them with horizontal and vertical variables - and you NEVER mix the horizontals with verticals. Time (t) is neither horizontal nor vertical - it is the same (t) for both dimensions.

Given an initial horizontal velocity (vox) of 12 m/s and vertical height (xy) of 5 m, find:

a. time to fall (t)

b. horizontal displacement (xx)