Conservation of Momentum and Relative Velocity

[whoareyou]

Homework Statement

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.
Answer: 0.25 m/s[E]

Homework Equations

Conservation of momentum (P = P')

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' = ?

 

[collinsmark]

Homework Statement

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.
Answer: 0.25 m/s[E]

Homework Equations

Conservation of momentum (P = P')

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 ?

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.)

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

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.)

 

[whoareyou]

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

 

[collinsmark]

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

Yes, that's right!

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

 

[whoareyou]

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

 

[collinsmark]

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

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.]

 

[whoareyou]

It works out! Thanks a lot! :D

 

[collinsmark]

There ya' go.