Finding initial velocity and theta, given range and height

[Seri]

Homework Statement

A stone is thrown down a slope. I am given the Range of the slope and the max height from spot thrown.
R= 50m
h= 12m

Homework Equations

I need to determine the magnitude of Vo and inital theta.

The Attempt at a Solution

First I need to find V_o:
I feel that the only relevant portion to find the initial velocity is from the spot thrown to the max height where V_yo is 0. I broke up the components of velocity so that:
V_xo=vcos(theta)
V_yo=vsin(theta)

However, I'm lost after this because I don't know t. My first idea was to find t, but I was having problems finding an equation that doesn't use v, theta, in a time equation.
My second idea was to find an equation that avoids time such as v_y^2=V_yo^2-g(y-yo).

I haven't attempted the initial theta part yet.

 

[Seri]

Reading through this post, this morning, I realized I forgot to add that the slope has a rise of 30m and a run of 40m. I don't feel that would help with find V_o though. :/

 

[baba89]

Your approach is correct. To find the initial velocity, you can use the fact that at the maximum height, the vertical component of velocity is 0. This means that V_yo=0 and V_xo=Vcos(theta). Using the equation V_y^2=V_yo^2-2gh, you can solve for V. Then, using the equation V_x=Vcos(theta), you can solve for theta.