A 45.0-kg girl is standing on a 153-kg plank. The plank, originally at rest, is

Question

A 45.0-kg girl is standing on a 153-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

momentum conservation:

m1v1 + m2v2 = 0

v1 = velocity of relative to ground = velocity of girl relative to plank + velocity of plank(which is v2)

so

45*(1.39+v2) + 153*v2 = 0

198v2 = -62.55

v2 = -.316 m/sec

a)

her velocity relative to ice = 1.39-.316 = 1.07 m/sec

b)

velocity of the plank relative to the surface of ice = v2 = -.316 m/sec

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