if a man of mass m jumps to the ground from height h and his centre of mass moves a distance d in the time taken by him to hit the ground show that the average force acting on him is mgh/d

Force is considered the change in potential energy, U, over a change in position, x. In other words it is the derivative of potential energy with respect to time.

F = dU/dx

here,U=mgh

change in position=change in position of centre of mass=d

 

so average force=mgh/d