# Calculate the initial velocities of buggies

1. Sep 20, 2012

### utkarshakash

1. The problem statement, all variables and given/known data
Two identical buggies 1 and 2 with one man in each move without friction due to inertia along the parallel rails toward each other. When the buggies get opposite each other, the men exchange their places by jumping in the direction perpendicular to the motion direction. As a consequence, buggy I stops and buggy 2 keeps moving in the same direction, with its velocity becoming equal to v. Find the initial velocities of the buggies v1 and v2 if the mass of each buggy (without a man) equals M and the mass of each man m.

2. Relevant equations
Momentum Conservation

3. The attempt at a solution
Let the buggy 2 move in the -ve X direction and buggy 1 in +ve X.
Along the direction of motion momentum conservation principle can be applied.
$P_{initial}=(m+M)v_{1}-(M+m)v_{2}$
$P_{final}=-(M+m)v$
From this I get a relation between three
$v_{2}=v_{1}+v$

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