A ball is dropped from 20.0 ft above the ground. At what height is half of its energy kinetic and half potential? Using enegry conversation only, what is the velocity of the ball just as it hits the ground?

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Since the KE = the PE at the requested height 2PE = total available energy = 20W where W is the weight of the object, presumably in pounds.  Too bad this isn't in SI units. Thus the PE is 10W at the requested height, but this is also Wh Wh = 10W so h = 10 feet.   In the second part of your question all of the available potential energy is converted to KE so 20W = (0.5*WV^2) / 32   since the acceleration due to gravity in the English system is 32 ft / s^2. W cancels out and V = 3.5.8 ft / s