What force does the water exert on the man?

What force does the water exert on the man?

• An 84 kg man drops from rest on a diving board 3.1 m above the surface of the water and comes to rest 0.52 s after reaching the water. The acceleration due to gravity is 9.81 m/s^2. What force does the water exert on the man? (Answer in units of N.) *Round your answer please, thanks*

• Answer:

  The speed when he reaches the surface is sqrt(2gh) with g the gravity and h the height. From there on, he is subjected to a vertical (upward) force of F-mg if F is the force the water exerts on him. Now the integral of this force with respect to time gives the momentum variation. (Fdt = mdv) So we must have (assuming a constant force) (F-mg)*T = m*sqrt(2hg) to bring him to rest. F = mg + m*sqrt(2hg)/T = 84(9.81 + sqrt(2*3.1*9.81)/.52) = 2084 N