A 50 kg girl is standing on a 150 kg plank. The plank, originally at rest, is fr

Question

A 50 kg girl is standing on a 150 kg plank. The plank, originally at rest, is free to slide on a frozen lake that is a flat, friction-less surface. The girl begins to walk along the plank at a constant velocity of 1.25 m/s to the right relative to the plank. Let the direction of the girl is moving in be positive and indicate the direction with the sign of your answer. What is the velocity of the plank with respect to the surface of the ice? What is her velocity with respect to the surface of the ice?

Explanation / Answer

This is a functionally isolated system so momentum is conserved.
v=speed of plank rel. to ice. m=mass of person
B=speed of person rel. to ice. M=mass of plank
v'=speed of plank rel. to person.
v'=v-B (galilean velocity transformation equation)
v=v'+B
Now, since p(i)=p(f) and p was initially 0
-M(v'+B)=mB
-Mv'-MB=mB
B=-Mv'/(m+M)
B=-150*1.25/(50+150)

B=0.937m/s ANSWER

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