# Theoretical Range Equation Derivation

1. Sep 19, 2007

### ccsmarty

1. The problem statement, all variables and given/known data

Derive an expression for calculating the theoretical range of the ball in terms of y, g, theta, and v0.

2. Relevant equations

3. The attempt at a solution

I've tried just about everything to figure this out. I started with the motion in the x-direction, and plugged the second-to-last equation in for v0x in the second equation, and then solved for "t". Then I plugged the "t" into the second equation (but for the y-direction), and tried solving for "x". But I kept getting really weird numbers. Can someone please help me out?

2. Sep 19, 2007

### mgb_phys

Motion in the x direction is at a constant speed, so what you are looking for is the time given by motion in the y direction.
Use s = ut + 1/2 at^2 and v^2 = u^2 + 2as to get an equation for time as a function of initial vertical velocity component. Remember that final (vertical) velocity is zero at the top of the curve.
Then plug this into the horizontal component of velocity to get a range.