Calculate average force of the mud in stopping the person

Question

A 58.5kg person falls 8.9m from a storage building and lands straight- legged in some mud. The person stops after sinking 0.4m into the mud. Calculate the average force of the mud in stopping the person.

Answer 1

You will solve this using energy. At the top of the storage building, the person has potential energy equal to P = mgh = (58.5 kg)(9.81 m/s^2)(8.9 m) = 5107.6 J. When he hits the mud (before sinking) he has kinetic energy E = 5107.6 J. When he comes to a stop, his kinetic energy is zero and the mud has done work equal to the initial energy. Remember, work is defined as the change in kinetic energy. Work is also equal to force times distance. So, the work done by the mud, W = 5107.6 J = F x d ==> F = W / d = (5107.6 J / 0.4 m) = 12769 N = 12800 N or 13000 N, depending on whether you need the answer to 3 or 2 significant figures.