Which Material Exerts Greater Impulse When Jumping Off a Dock?

[Maxo]

Homework Statement

Suppose you are standing on the edge of a dock and jump straight down. If you land on sand your stopping time is much shorter than if you land on water. Using the impulse-momentum theorem as a guide, determine which one of the following statements is correct:

a) In bringing you to a halt, the sand exerts a greater impulse on you than does the water.

b) In bringing you to a halt, the sand and the water exert the same impulse on you, but the sand exerts a greater average force.

c) In bringing you to a halt, the sand and the water exert the same impulse on you, but the sand exerts a smaller average force.

Homework Equations

J = m*(Vf-V0)

The Attempt at a Solution

Let's say we have mass = 100 kg, v0 = -10 m/s and vfw = -2 m/s for water and vfs = 0 m/s for sand. Then the impulse in each case would be J = m(Vf-V0) = 100*(-2-(-10))=800 Ns for water and J = 100*(0-(-10))=1000 Ns for sand.

So this seems to give a greater impulse for sand. However my book says the answer is b). Is there something wrong with my calculation? Isn't J=m*(Vf-V0) the equation for impulse?

 

[George Jones]

In bringing you to a halt

Is the above consistent with

vfw = -2 m/s for water