Please be legible on paper (if provided) and please explain the reasoning behind

Question

Please be legible on paper (if provided) and please explain the reasoning behind each steps.

As Henri LaMothe (in his 70's) (mass m) in the circus is performing his belly-flop into a very shallow pool of water (depth d), he jumps off one of the very tall (height h) platforms used by the trapeze aerialists. a) If the water is just barely deep enough to keep the clown from striking the bottom of the pool, show that the average force on the clown due to the water is given by F = mgh/d. Show that the impulse on the clown due to the water is given by

Explanation / Answer

uisng energy conservation,

work done by gravity = work done by water force

mg(h+d) = <F> . d

<F> = mgh( 1 + d/h) / d     here h >>>d

so d/h just approach to zero. so 1 + d/h =1

<F> = mgh/d

b) impusle = change in momnetum

final velocity = 0

initial velicty= v

using energy conservation,

mgh = mv^2 /2

v = sqrt(2gh)

impulse = m ( sqrt(2gh) - 0) = m sqrt(2gh)

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