Please show all work and make sure that the work can be easily to read and under

Question

Please show all work and make sure that the work can be easily to read and understand. Also please answer all the parts. Thank you very much. 1. A girl of mass mg is standing on a plank of mass m. Both are originally at rest on The girl begins to walk along a frozen lake that constitutes a frictionless, flat surface. the plank at a constant velocity Ugp to the right relative to the plank gp denotes the girl relative to plank.) . (The subscript ank at a constant velocity vpp to the right relative to the plank. (The subscript (a) What is the magnitude of the velocity pi of the plank relative to the surface of the ice? [4 pts] (b) What is the magnitude of the girl's velocity Vol relative to the ice surface? (4 ptsl (c) If the girl walks a distance a along the plank and then stops, how far does the plank move relative to the surface of the ice? [3 pts] (d) How far does the center-of-mass of the girl-plank system move relative to the ice? [2 pts

Explanation / Answer

a)
Since no external force is applied, momentum is conserved.
Initial momentum = 0
Momentum when the girl starts walking with a velocity Vgi relative to ice,
Final momentum = Mg Vgi + Mp Vpi
Since momentum is conserved, Mg Vgi + Mp Vpi = 0
Vpi = [Mg/Mp] Vgi

b)
Girls velocity relative to ice = Velocity of plank relative to ice + Girl's velocity relative to plank
Vgi = - Vpi + Vgp
Substituting for Vpi
Vgi = - [Mg/Mp] Vgi + Vgp
Vgi [1 + (Mg/Mp)] = Vgp
Vgi = Vgp / [1+ (Mg/Mp)]

d)
Since there is no external force is acting, center of mass will remain stationary.

c)
If the plank's center of mass moved a distance of Xp distance,
Mg x = Mp Xp
Xp = (Mg/Mp) x

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