Solving for initial velocity Projectile Motion

[clark1089]

Homework Statement

A rock is thrown from the top of a twenty meter high building at the angle 53 degrees above the horizontal. IF the horizontal range of the throw is equal to the height of the building, what is the speed of the rock? How long is it in the air? What's the velocity of the rock before it hits the ground?

Homework Equations

Vx = Vox
Vy = Voy - gt
x = xo + Voxt
y = yo + Voy - (1/2)gt^2

The Attempt at a Solution

I use the second one and set x = to 20 and solve for the time...

20 = 0 + Vcos(53)t
t = 20/Vcos(53)

I substitute into the y equation

20 = vsin(53) - 1/2g(20/vcos(53)^2

Here is where I think I'm making the big mistake... help! :(

 

[rl.bhat]

The displacement y is along g. So it must be -ve
So rewrite the equation and solve for v.