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. Thank you very much.
mass mg is standing on a plank of mass Both are originally at rest on frictionless, flat surface. The girl begins to walk along o the right relative to the plank. (The subscript 1. A gir l of mass mg is standing on a frozen lake that constitutes a fric the plank at a constant velocity vgp to the right relative to the p gp denotes the girl relative to plank. (a) What is the magnitude of the velocity pi of the plank relative to the surface of e magnitude of the velocity tpl of the plank relative to the surface of the ice? [4 pts] (b) What is the magnitude of the girl's velocity vgi relative to the ice surface? [4 ptas (c) If the girl walks a distance r 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) suppose plank moves with velocity Vp in relative to ice surface in opposite direction.

Vgp = velocity of girl relative to surface - Vp

Vg = Vgp + Vp

intially momentum of plank-girl system was zero.

using momentum conservation,

0 = mg ( Vgp + Vp) - mpVp

Vp ( mp - mg ) = mg Vgp

Vp = mg Vgp / (mp - mg)

b) Vgp =Vg - Vp

Vg = Vgp + Vp = Vgp + mg Vgp / (mp - mg)

Vg = (mp Vgp - mg Vgp + mg Vgp) / (mp - mg )

Vg = mp Vgp / (mp - mg)

c) position of centre of mass plank-girl system will not change.

suppose plank moves distance d in opposite direction.

0 = mg (x - d) + (mp)(- d)

mgx = (mg + mp)d

d = mg x / (mg + md)

d) centre of mass of system doesn't move.

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