Coefficient of restitution?

Question

I know the formulas for the coefficient of restitution are:

Cr = V(final)/Velocity(initial) and:

Cr = sqrt(bounce height/drop height)

but what is the working for getting to the Cr = sqrt(bounce height/drop height) from using Cr = V(final)/Velocity(initial). I know you have to use PE = mgh and all that.

Thanks

Answer 1

h1 = v1^2/(2g)
h2 = v2^2/(2g)
h2/h1 = v2^2/v1^2
v2/v1 = √(h2/h1) = Cr