# Need help with Physics word problem dealing with Momentum

1. Oct 11, 2005

### Taren

Alright, First I'll explain the problem, then I'll explain what I've tried and what's confusing me.

A 45.0 kg girl is standing on a 150 kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.50 m/s to the right relative to the plank. (A) What is her velocity relative to the ice surface? (B) What is the velocity of the plank relative to the ice surface?

Keep in mind that the preceeding paragraph is completely quoted from my textbook, so none of my assumptions are in it. Everything above is fact. I've looked through my lecture notes and my text book, and I can't figure out this one...It's in our chapter dealing with momentum, so I kinda figured I'd plug all the variables into the formula for conservation of momentum. Doing that, I determined that the Plank was moving with a velocity of -.45 m/s while the girl was walking, moving against her velocity...I thought to find the answer to (A) all I'd have to do would be to subtract the plank's velocity from the girls velocity, I.E: 1.50 m/s - .45 m/s, which gave me the answer 1.05 m/s for the girl's velocity relative to the ice surface. But when I checked the book's answer, it said her velocity relative to the ice surface is 1.15 m/s. I don't know what I'm doing wrong, and I'm terribly confused...can someone please help me?

2. Oct 17, 2005

### Tom Mattson

Staff Emeritus
Sorry for the late reply. If you're still interested, here are my comments.

Word of advice: Don't treat physics problems in a "plug-n-chug" fashion. Think about what you're doing.

How did you arrive at that number? It's impossible to spot any errors you might have made without seeing your work.

You are indeed going to subtract two velocities, but you have to make sure that you don't mix up velocities from two different reference frames in your analysis. I suspect that that's what you did, but without seeing your steps I can't know for sure.

3. Dec 5, 2007

### FrixioN911

Wow, I'm wondering this too - how the book got 1.15.

Tom, or anyone else willing to help:

M(girl)V(girl)[initial] + M(plank)V(plank)[initial] = M(girl)V(girl)[final] + M(plank)V(plank)[final]

So: 0 + 0 = (45)(1.50) + (150)(V)
So: 0 = 67.5 + 150(V)
So: 67.5 = -150(V)
So: V = -.45 <--- Final Plank velocity.

So if the girl is 'moving' 1.50 m/s, and the plank is moving -.45 m/s -- wouldn't her velocity relative to the ice be 1.50 - .45 = 1.05 ??

What is wrong here? Taren said the book stated the answer as 1.15