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## Homework Statement

A 62.7-kg woman contestant on a reality television show is at rest at the south end of a horizontal 141-kg raft that is floating in crocodile-infested waters. She and the raft are initially at rest. She needs to jump from the raft to a platform that is several meters off the north end of the raft. She takes a running start. When she reaches the north end of the raft she is running at 4.78 m/s relative to the raft. At that instant, what is her velocity relative to the water?

[tex]v[/tex] = velocity of contestant with respect to the water

[tex]v_{r}[/tex] = velocity of contestant with respect to the raft

[tex]V[/tex] = velocity of raft with respect to the water

[tex]m[/tex] = mass of contestant

[tex]M[/tex] = mass of raft

## Homework Equations

[tex]P_{I} = P_{f}[/tex]

[tex]V=v-v_{r}[/tex]

## The Attempt at a Solution

Here is my derivation and equation but I'm not getting the right answer! Where did I go wrong?

1. [tex]P_{I} = P_{f}[/tex]

2. [tex]0=MV+mv[/tex]

We don't know V so I substitute with:

[tex]V=v-v_{r}[/tex]

3. [tex]0=M(v-v_{r}) + mv[/tex]

Now solve for v (speed of contestant relative to water)

[tex]v=\frac{Mv_{r}}{M+m}[/tex]

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