A girl of mass m G is standing on a plank of mass m P . Both are originally at r

Question

A girl of mass mG is standing on a plank of mass mP. Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity vGP to the right relative to the plank. (The subscript GP denotes the girl relative to the plank.)

(a) What is the velocity vPI of the plank relative to the surface of the ice? (Use the following as necessary: vGP, mG, and mP. Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.)

(b) What is the girl's velocity vGI relative to the ice surface? (Use the following as necessary: vGP, mG, and mP. Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.)

Explanation / Answer

1) as the velocity of the center of mass of the girl+plank system does not change because there is no external force, the speed after the girl walks and speed before the girl walks is same i.e. 0. (because initially the system was at rest)

so let the speed of plank relative to surface of ice be vPl.

then speed of the girl relative to surface of ice=vG=vGP+vPl

then using speed of center of mass=0

mG*(vGP+vPl)+mP*vPl=0

vPl=-mG*vGP/(mP+mG)....(ans)

as you see , there is a -ve sign that means the plank will move in opposite direction to the girl.

b)girls velocity with relative to surface of ice=vGP+vPl=vGP-(mG*vGP/(mP+mG))

=mP*vGP/(mP+mG)

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