# How to work out momentum when there are velocity and mass changes

I have a pretty simple homework question, but I can't rap my head around it.

In the question a swimmer of $55 \mbox{ } \mathrm{kg}$, jumps off a stationary raft of $210\mbox{ }\mathrm{kg}$. The swimmer jumps off the raft with a speed of $4.6 \mbox{ } \mathrm{ms}^{-1}$. I need to work out the recoil velocity of the raft.

So because Momentum before = Momentum after, I went:

$p_i = 0$

Therefore $0 = p_f$ and $p_f = mv$, $m = 210\mbox{ }\mathrm{ }$, so the $v$ would have to equal $0$. Making the recoil velocity equal $0$. However that doesn't seem right. Could use some clarification or help, thanks.

• Seriously, Pi = 0? : ) P.S. Thank you for showing your work and what you've done so far . in a hw problem . Aug 3 '13 at 11:26

So your equation should be $$P_{i,system}=P_{f,system}$$ $$0=m_{raft}\vec v_{raft}+m_{swimmer}\vec v_{swimmer}$$
Also note that $v_{raft}$ and $v_{swimmer}$ are the velocities in the ground frame. The $4.6 m/s$ of the swimmer might be with respect to the raft. So you'll have to convert that velocity to the ground frame velocity.