Question on conservation of momentum

[lilmul123]

Homework Statement

A 56-kg woman contestant on a reality television show is at rest at the south end of a horizontal 147-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 4.6 m/s relative to the raft. At that instant, what is her velocity relative to the water?

Homework Equations

Psystem = Pwoman + Praft = 0

Pwoman(f) - Pwoman(i) + Praft(f) - Praft(i) = 0

The Attempt at a Solution

I've split up the momentums into their each individual parts. The mass of the woman is 56kg, the raft is 147kg, and this is where I'm stuck. I believe that Pwoman(i) and Praft(i) are 0 because they both are initially at rest. Now I have Pwoman(f) + Praft(f) = 0. I don't know where to plug in her speed (Pwoman or Praft?), and either way, I would get a negative answer. Can someone help me figure out where to go from here?

 

[tiny-tim]

Hi lilmul123!

In questions about relative velocities, you really need two subscripts, not one.

Call the woman j, the raft r, and the water w.

[STRIKE]Then P_jw, for example, would be the momentum of the woman relative to the water.

And P_jw = P_jr + P_rw.[/STRIKE]

Then V_jw, for example, would be the velocity of the woman relative to the water.

And V_jw = V_jr + V_rw.

 

[lilmul123]

How do I figure out the speed of the raft relative to the water?

 

[tiny-tim]

How do I figure out the speed of the raft relative to the water?

(On second thoughts, my last post was rather confusing when it talked about momentum, so I've edited it )

The question gives you V_jr.

So find a physics equation relating V_jw and V_rw,

and combine it with the geometry equation V_jw = V_jr + V_rw.