Optimal launch angle for projectile from a curved surface

[TedGramm]

Homework Statement

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

Homework Equations

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

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

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.

 

[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