# Homework Help: Projectile Fired Against Sloped Surface

1. Oct 23, 2008

Lets say a Projectile is fired at an angle (theta) from the Horizontal. The Catch is that the place it was fired from is a hill sloped angle (phi) against the horizontal. The question is what are the angles are which you can get the highest Range (Range = not the Farthest Horizontal Distance, but the farthest distance along the slop).

Hint: If (phi) is 60, then (theta) is 15.

I've tried doing this problem multiple ways. I set the slope length as D. Making the Vertical displacement vector at the end -Dsign(phi), and the Horizontal Displacement Vector Dcos(phi).

I then used the basic Kinematics equations and combined them. I solved for t under the horizontal displacement and plugged in what I got into my vertical displacement equation, but I keep going nowhere because I have a bunch of sines and cosines with theta and phi.

Can anyone save me?

I understand if the ground was flat, the answer would be 45 Degrees as the firing angle, but... with the slope it is VERY different.

Last edited: Oct 23, 2008
2. Oct 24, 2008

### tiny-tim

Welcome to PF!

(have a theta: θ and a phi: φ )

Show us your θ and φ equations … there's probably a simple trig trick for solving them (like the sin(A+B) rule).

3. Oct 31, 2008