How to Calculate the Range of a Projectile on a Sloped Surface?

[Newton's Protege]

I was hoping someone might be able to help with this. I have provided the problem and everything I know about solving it. Any help will be appreciated.

A projectile hits a slope at a certain point. What is the range of the projectile along the slope?

Given: initial velocity (V sub-zero), the angle alpha, the angle Beta, and g (free fall acceleration constant).

Find R (range):

Apparently, the following equation will find the range of the projectile if it hit the ground instead of a slope above the ground:

R= (initial velocity squared)(sine 2angle theta)/g

Is there a specific equation to solve for the range of a projectile when it hits a slope rather than the ground?

The equations of two dimensional motion must be used to derrive this equation. It has something to do with finding y as a function of x (y(x)). The following equation must be used: x=(initial velocity multiplied by the cosine of angle theta) multiplied by time(t). Time must be eliminated from the equation yielding time=x/inititial velocity(angle alpha+angle beta).

Thank You everyone

 

[Pyrrhus]

Start by setting up the "slope equation" (straight line), it should be of the form y = mx + b. Now recall that when the projectile hits the slope, the trajectory equation of the projectile will have the same Y as our straight line. To get the range you can use the distance equation of 2 points in a cartesian plane.