Rifleman's Rule: Best angle for a projectile up a hill [ ]

[FissionMan1]

Rifleman's Rule: Best angle for a projectile up a hill [urgent]

Homework Statement

A projectile is fired at speed Vo at an elevation angle alpha up a hill of slope beta (alpha>beta). At what angle will the range (L) be maximum?

Homework Equations

L=(2Vo^2)/g*(cos(a)/cos(b))*(sin(a)-cos(a)tan(b)) is the distance up the slope that

The Attempt at a Solution

From the above equation we can see that if b=zero, we can maximize the equation by making a=45. If a=b, L=0. The question is, how do we make an equation that maximizes L. I tried integrating and setting the LHS to zero, but that didn't work. I need a relationship between L, b, and a that maximizes.

I'd like no full answers here since it is a homework question, just help as to how to find the relationship.

 

[FissionMan1]

Nevermind! The problem is solved. For future reference, you merely take the derivative of the L equation with respect to alpha. Do a few trig identities in order to get one alpha in the equation and solve.

 

[turbo]

Can anyone generalize and explain why shooting on a steep up-slope or down-slope might result in an error in elevation? Why might the error be equivalent?