Walking on a board over ice (EK FL #1H)

[IRASNA]

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My camera doesn't work otherwise I'd post the picture associated with this problem. Basically there's a frictionless ice surface labelled from -2 on the left to +2 on the right. The board sits between 0 and +2, with a man standing on the left end of the board (at 0). Here's the question:

A 100 kg man stands on the left end of a 100 kg board 2m long which sits on a frictionless surface as shown above. Where will the left end of the board come to rest if the man walks to the right end of the board and stops?

A. -2
B. -1
C. 0
D. +2

Answer: B. -1
(highlight for answer)

Explanation says something about conserved momentum and center of gravity at 0.5? I understand how they get the center of mass at 0.5, but how do you set this up (easily) on test day? Help? Thanks

 

[gentlebeast]

I would answer it with conservation of momentum.
suppose the board moves x to the left, then the man moves 2-x to the right
100x=100(2-x)
x=1
the left end of board is -1

 

[Arctangent]

With this question , you can consider point masses centered at 0 (the man) and at +1 (the board) that have equivalent mass. After the movement, the man is centered at +1. For conservation of momentum, the board must necessarily be centered at 0. In other words, the two equivalent point masses have switched places. If the board is centered at 0, the left end is at -1.