Projectile Motion and Prime Axis

[kathmill]

The Problem
A projectile is thrown from a sloping hill with an initial speed of 20m/s directed perpendicular from the slope. If the incline of the slope is 32 degrees, how far from where it is thrown will the ball land?

I found these equations will result in a solution...
Want: R = square root of: (change in x)^2 + (change in y)^2 (pythagorean)
delta X= 1/2Axt^2
delta Y= Vyt + 1/2Ayt^2

tan(angle) = delta y/delta x

BUT...
where do I find Ax and Ay with the prime system?

 

[LowlyPion]

I think finding the solution through ordinary means in the x,y is probably a little easier than translating the axes.

If the initial velocity is perpendicular to the incline then you have your angle of launch and the component velocities readily enough.

If you treat then the incline as a function such that y = m*x where m is the slope, you can solve for the intersection of the trajectory and the slope.