# Homework Help: Conservation of Momentum and Relative Velocity

1. May 17, 2012

### whoareyou

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

A 55kg student stands on a 4.6 kg surfboard moving at 2.0 m/s [E]. The student then walks with a velocity of 1.9 m/s[E] relative to the surfboard. Determine the resultant velocity of the surfboard, relative to the water. Neglect Friction.

2. Relevant equations

Conservation of momentum (P = P')

3. The attempt at a solution

I plugged in the values given (relative to the water) into the equation, but I'm not getting the right answer ?

ms = mass of student
mb = mass of board
vs = 2.0m/s
vb = 2.0m/s
vs' = 1.9m/s + 2.0m/s
vb' = ?

2. May 17, 2012

### collinsmark

Your top equation is correct. But before solving for v'B, you'll need to correct a mistake.

(The bottom equation is technically correct too, but it's too early to solve for v'B. Solving for it at this point doesn't make the problem easier.)
The error is your
vs' = 1.9m/s + 2.0m/s​
equation. That's not right.

The way you've expressed the equation, the board maintains its 2.0 m/s velocity even after the surfer starts walking. But that's not right. The board has a different velocity when the surfer is walking. You need to replace that 2.0 m/s with with the new velocity of the board. (Hint: the new velocity of the board is a variable that you haven't solved for just yet.)

3. May 17, 2012

### whoareyou

But isn't the new velocity of the board what we're trying to solve for?

4. May 17, 2012

### collinsmark

Yes, that's right!

(Another hint: you have a little more algebra to do. )

5. May 17, 2012

### whoareyou

So then if 2.0m/s is not the final velocity of the surfboard, then it would be 1.9m/s + vb' ?

6. May 17, 2012

### collinsmark

No not quite.

But the student is walking at 1.9 m/s relative to the board.

So that means the velocity of the student is v's = 1.9 m/s + v'b.

[Edit: I was calling the student a 'surfer'. Changed it back to 'student' in this post.]

7. May 17, 2012

### whoareyou

It works out! Thanks a lot! :D

8. May 17, 2012

### collinsmark

There ya' go.