# Maximizing range of projectile from some curve

1. Sep 7, 2010

### TedGramm

1. The problem statement, all variables and given/known data
A projectile is launched from the top of some function (pick one other than a line)
For a given speed, find the launch angle to maximize the range

2. Relevant equations

projectile parabola equation (I haven't figured out latex yet t_t )

y = x*tan(theta) - (g/2)*(x/( v*cos(theta) ))^2

3. The attempt at a solution

I tried sinx, cosx, e^x and x^2, set up so they look look like a downward sloping hill from the origin

First I equate the projectile equation with whichever function I'm trying to the projectile parabola, then I differentiate implicitly with respect to theta. I solve for dx/d(theta), set this to zero, and solve for theta.

With the first three, I end up with theta = arctan(v^2 / gx), for the parabola, I end up with a trig equation that I can't solve.

That the first three end up with the same answer seems a little fishy, was just wondering if anyone had any experience with a problem like this.

Last edited: Sep 7, 2010
2. Sep 8, 2010

### ehild

The projectile launches from the top of a function. The function has to decrease from x=0. You need to add a term f(0) to the equation for y. Than set y=f(x) to find the place xm where the projectile reaches the function. Find the maximum of xm with respect to theta. Be sure that you differentiate properly. Show your work.

ehild

Last edited: Sep 8, 2010