How Long Does It Take for a Ball Launched Off a Cliff to Hit the Ground?

[TheDoorsOfMe]

Homework Statement

Ok, you have a cliff with height h and you launch a ball off of it at speed v and angle $$\theta$$. How long till it hit the ground?

Homework Equations

(1) Vsin($$\theta$$) = V$$_{y}$$
(2) V$$_{f}$$ = V$$_{y}$$ + at
(3) d = ((V$$_{i}$$ + V$$_{f}$$)/2)*t

The Attempt at a Solution

Ok, so what I did was take equation (2) and set V$$_{f}$$= 0. This alllows me to solve for the time that it takes to reach peak. Multiply this result by 2 to get the time when the ball is back to the plane of the cliff. Then for the time down to the ground I used equation (3) and plugged in V$$_{f}$$= $$\sqrt{V^{2}_{i}+2gh}$$ for V$$_{f}$$. Then I solved for t.

This lead to a result I feel looked to complicated for the question. Did I do this right?

Homework Statement

Homework Equations

The Attempt at a Solution

 

[TheDoorsOfMe]

Ok, I don't know why all my subscripts look like superscripts in this but they do. All those i's and f's are for intial and final velocity.