A 45.0-kg girl is standing on a 143-kg plank. The plank, originally at rest, is

Question

A 45.0-kg girl is standing on a 143-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 1.35 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

Mass of the plank=M = 143 kg
Mass of the girl= m = 45 kg
velocity of the girl relative to the plank, v1 = 1.35 m/s
let the velocity of the plank plus girl = v2

initial momentum of planck plus girl=0 as both are at rest

using the law of conservation of momentum,final momentum= initial momentum
(M+m)v2+mv1 = (M+m)0

(M+m)v2 = -mv1
v2 = -(45 *1.35)/(143+45)
v2 = -0.323 m/s

a) velocity of girl relative to ice surface = v1+v2 = 1.35+-.323 = 1.03 m/s
b) velocity of plank relative to ice surface = v2 = -0.323 m/s

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