Using standard formulae, derive an expression for the final speed of a falling object in terms of its change in height. Assume zero air resistance or other resistive forces.

Ek = (1/2)mv2

Ep = mg(dh)

Set these equal to each other, because of conservation of energy:

(1/2)mv2 = mg(dh)

Cancel the mass:

(1/2)v2 = g(dh)

v2 = 2g(dh)

v = (2g(dh))1/2

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