A 45.0 kg girl is standing on a 150 kgplank. The plank, originally at rest, is f

Question

A 45.0 kg girl is standing on a 150 kgplank. The plank, originally at rest, is free to slide on a frozenlake, which is a flat, frictionless surface. The girl begins towalk along the plank at a constant velocity of 1.52 m/s relative to the plank. (a) What is her velocity relative to thesurface of ice?
1 m/s

(b) What is the velocity of the plank relative to the surface ofice?
2 m/s (a) What is her velocity relative to thesurface of ice?
1 m/s

(b) What is the velocity of the plank relative to the surface ofice?
2 m/s

Explanation / Answer

Mass of the girl is m = 45 kg Mass of the plank is M = 168 kg combined velocity is v 1 +v2 = 1.51 m/s from momentum of conservation  m1 v1 = m2 v2     m ( 1.51 m/s - v2 ) = M v2                         -v2 = m / m + M ( 1.51 m/s )                                   = 45 kg / 45 kg + 168 kg * ( 1.51 m/s )                                  v2  = - 0.3190 m/s   ( velocity of the plank relative to ice)                               v 1 = 1.82 m/s ( her velocity relative tosurface of ice )

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