A 45.0-kg girl is standing on a 166-kg plank. The plank, originally at rest, is

Question

A 45.0-kg girl is standing on a 166-kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.39 m/s to the right relative to the plank. (Let the direction the girl is moving in be positive. Indicate the direction with the sign of your answer.) (a) What is her velocity relative to the surface of ice? ___________m/s (b) What is the velocity of the plank relative to the surface of ice? ____________m/s

Explanation / Answer

a] The initial momentum of the system = 0

[since both the girl and the plank are at rest]

the momentum of the system must be conserved.

45v + 166V = 0

Also, since the girl later walks with a velocity of 1.39 m/s to the right with respect to the plank,

v - V = 1.39

=> V = v - 1.39

substitute this above to get:

45v + 166[v - 1.39] = 0

=> v = 1.0935 m/s

this is the velocity of the girl with respect to ice.

therefore, V = 1.0935 - 1.39 = - 0.2964 m/s

this is the velocity of the plank with respect to the ice.

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