Question on conservation of momentum

[lilmul123]

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

Psystem = Pwoman + Praft = 0

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


3. 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! :smile:

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

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

Then Pjw, for example, would be the momentum of the woman relative to the water.

And Pjw = Pjr + Prw.

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

And Vjw = Vjr + Vrw. :wink:

[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 :redface:)

The question gives you Vjr.

So find a physics equation relating Vjw and Vrw,

and combine it with the geometry equation Vjw = Vjr + Vrw. :smile: