A projectile is fired with initial speed v0 at an elevation angle (alpha) up a hill of slope (beta) (alpha > beta).
a) How far up the hill will the projectile land?
b) At what angle (alpha) will the range be a maximum?
c) What is the maximum range?
x = v0tcos(alpha)
y = -(gt^2)/2 + v0sin(alpha)
r = (x^2 + y^2)^(1/2)
The Attempt at a Solution
I had thought that the solution to this problem might be as simple as finding where the line that represents the hill intersects with the line that represents the trajectory of the projectile. But I'm not sure how to get there from here. I would know how to solve this if the range I was concerned about was the range from where the projectile is launched to where it hits the ground again (i.e. y2 = 0), but this has me stumped. Anything to point me in the right direction would be appreciated!