Horizontal Projectile Motion, initial velocity equation?

Question

A ball is thrown horizontally from a height h above the ground and hits the ground with a speed that is n times its initial speed. Derive a formula for the initial speed vo in terms of g, h, and n.

Answer 1

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Using conservation of energy:

mgh+(1/2)mv^2=(1/2)m(nv)^2

2gh+v^2=(n^2)(v^2)

2gh=(n^2)(v^2)-v^2

2gh=(n^2-1)(v^2)

v^2=2gh/(n^2-1)

v=sqrt(2gh/(n^2-1))