How Do You Calculate the Final Velocity of a Projectile?

[vinamas]

Homework Statement

A rock is thrown from a cliff that is 50m long with an initial velocity of 7m/s and an angle of 53, find the rock's veloctity before it hits the ground

Homework Equations

vfy=sin(theta)*vi-gt
vf^2=(vi*sin(theta))^2-2gy

The Attempt at a Solution

x=vi*cos()t
t=x/(vi*cos)
x=7*cos(53)-2*9.81*(x/(vi*cos(53)))^2
x =2.49 or x=-6.11
at this point i tried to plug in x into vf^2=(vicos)^2-2gy
but none of them give 32 m/s which is the answer according to the answer's sheet

 

[brainpushups]

Some questions for you to consider:
In your solution what is x? It appears you are using x to represent two different quantities.
Why do you think the time of flight is given by your second equation?