# Momentum and Relative Velocity

## Homework Statement

A 56-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 4.0 m/s relative to the raft. At that instant, what is her velocity relative to the water?

## Homework Equations

p=person w=water r=raft
Vp = Vpr + Vrw

m*v(i) = m*v(f)

## The Attempt at a Solution

Using conservation of momentum
0 = 56 * 4 + Vr*141
Solving for Vr = -1.59 m/s

Vp = 4-1.59 = 2.41 m/s which is apparently wrong and I cannot see why it would be, any help would be appreciated

## Answers and Replies

Andrew Mason
Science Advisor
Homework Helper
The momentum of the woman + raft does not change. Therefore:

$$m_p\vec{v_{p:w}} + m_r\vec{v_{r:w}} = 0$$

where the :w means the velocity relative to the water.

To find the velocity of the woman relative to the water you have to use the relation:

$$\vec{v_{p:r}} + \vec{v_{r:w}} = \vec{v_{p:w}}$$

AM