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 plank. Use any variable or symbol stated above as necessary.)

(a) What is the velocity vpi of the plank relative to the surface of the ice?

(b) What is the girl's velocity vgi relative to the ice surface?

3 answers

The total momentum remains zero and the center of mass remains in the original location.

(a) The plank's velocity (relative to ice) is vpi. The girl's velocity relative to ice is vgp + vpi

Mp*vpi + Mg(vgp + vpi) = 0
vpi (Mg + Mp) = -Mg*vgp
vpi = -[Mg/(Mg+Mp)]*vgp

(b) vgi = vgp + vpi
= vgp{1 - [Mg/(Mg+Mp)]}
= vgp*[Mp/(Mg +Mp)]

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