A 200 lb. circus performer jumps from a 20 foot ladder onto a teeter-totter, launching a 50 lb. child. Assume a perfect transfer of energy, with no friction or air resistance. In his arc of travel, the child lands 50 feet horizontally to the rear. What was the total height the child achieved?

Question

A 200 lb. circus performer jumps from a 20 foot ladder onto a teeter-totter, launching a 50 lb. child.  Assume a perfect transfer of energy, with no friction or air resistance.  In his arc of travel, the child lands 50 feet horizontally to the rear.  What was the total height the child achieved?

anonymous · Answer

I know the following: $$E _{T} = E _{P} + E _{K}$$$$E _{P} = wh$$$$E _{K} = 0.5mV ^{2}$$From what I calculated, the total energy equals 4,000 ft-lbs, and since we're assuming a perfect transfer of energy, the child is also going to feel 4,000 ft-lbs of energy.  Therefore, the child should achieve a height of 80 feet going straight up.  However, I'm not sure how to take the 50 feet of horizontal travel into consideration and adjust the actual total height accordingly.