How Is the Horizontal Distance of a Cannon Ball Calculated on a Sloped Surface?

[msadegian]

A cannon ball is fired from an angle o with an intial velocity of v. The hill sklopes down with an angle of O. Prove that the horizontal distance the cannon ball travels is given by dx= 2v²cos(o)sin(O+o)/gcos(O)



2. Equations
sin(O+o)=sin(O)cos(o)+sin(o)cos(O)
d=1/2gt²

The Attempt at a Solution

Please help me! Hopefully the picture helps!

 

[LowlyPion]

Welcome to PF.

You might want to consider the point at which it hits as the intersection of the function that describes the projectile's flight with the equation that describes the slope of the incline.

For instance for 45 degrees you know that dx = dy.

Or more generally for angle θ you have Dy = tanθ *dx