Vf = 0.88 m/s Solving Momentum Question: 82kg Girl & 46kg Boy on Skateboard

[niki4d]

Homework Statement

A 82kg girl is coasting along the floor on a large 2.0kg skateboard. If she is moving 1.8 m/s when a 46kg boy jumps on to the same skateboard, what is the speed of the skateboard immediately after the boy jumps on it?

Homework Equations

Sum of Initial Momentum = Sum of Final Momentum

The Attempt at a Solution

This question looked pretty easy.. but I am sure I am doing something wrong... here's what I did so far:
(84kg)(1.8m/s) + (130kg)(0m/s) = (84kg + 130kg)Vf

 

[niki4d]

Sorry.. forgot the last part..
I got vf=0.7065m/s

Im not sure if this is right or not.. it SEEMS like an okay speed.. but I havn't done this type of question before.. so just want to be sure. Thanks!

 

[Gib Z]

(84kg)(1.8m/s) + (130kg)(0m/s) = (84kg + 130kg)Vf

You should only be looking at the initial and final momentums of the skateboard (and what ever is on it).

So it starts off with a total mass of 84 kg, going at 1.8 m/s. At the end, It has the mass of a 46 kg boy, so the total mass is 130 kg, and v_1 m/s is what we are trying to find. Equating both sides and making v_1 the subject;

$$84 kg \cdot 1.8 ms^{-1} = 130 kg \cdot v_1 ms^{-1}$$

$$v_1 = \frac{84 \cdot 1.8}{130}$$

I can already tell that's larger than one, so recheck your answer =]

 

[niki4d]

Hmm.. that makes sense.. but the answer to that would be 1.163m/s. The answer is 0.97m/s. I don't know how to get to that..

 

[Gib Z]

Well, That is somewhat odd...I think it's an error in the textbook, but it has been a while since I've studied Physics so I recommend you wait for someone who has more knowledge in this area to confirm.

 

[mjsd]

unless there are something else in the problem we have not addressed, otherwise I believe Gib Z's correct.

 

[niki4d]

Yeah.. more than likely it is.. thanks for the help!