A 121 kg physics professor has fallen into the Grand Canyon. Luckily, he managed to grab a branch and is now hanging 73 m below the rim. A student (majoring in linguistics and physics) decides to perform a rescue/experiment using a nearby horse. After lowering a rope to her fallen hero and attaching the other end to the horse, the student measures how long it takes for the horse to pull the fallen physicist to the rim of the Grand Canyon. The acceleration of gravity is 9.8 m/s^2.
If the horse’s output power is truly 1 horsepower (746 W), and no energy is lost to friction, how long should the process take?
Answer in units of s
Let's make some denotations: M = 121 kg; H = 73 m ; P = 746 W; g = 9.8 m/s²;
The work necessary to pick the professor up is A = mgH = 121*9.8*73 = 86563.4 J. So, it will take T = A/P = 86563.4/746 = 116.037 s.