Question

A stone was dropped off a cliff and hit the ground with a speed of 144 ft/s. What is the height of the cliff?

Answer 1

Using the kinematics equation for an object falling at a distance in the y direction with a velocity.

Y=Yo+VoT-(1/2)AT^2

and

Using the equation for Vfinal and Vinitial
V = Vo - AT

Since our Vo is 0, which we can assume given they didn't tell us the starting velocity.
and our Vfinal is given we can plug it into the equation and solve for t.

Then in the for Yfinal and Yintial we say
Yfinal = 0
and Yintial = y //where y is just some height that we started from

0 = y + 0 - (1/2)AT^2

The only unknown variable is y.
Solve for y that is your intial height.

I don't believe i made any conceptual mistakes let me know if I did.