A 45.0-kg girl is standing on a 169-kg plank. The plank, originally at rest, is

Question

A 45.0-kg girl is standing on a 169-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 1.60 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)Momentum is conserved. Let her velocity relative to ice is x and plank's velocity is y Then given x-y = 1.6 Initial momentum = final momentum =>0 = (45*x+(169*y) =>0 = 45*x + 169*(x-1.6) =>(45+169)x = 169*1.6 =>x=1.26355 m/s to the right b)x-y = 1.6 =>y = x-1.6 = -0.33645 m/s the velocity of the plank relative to the surface of ice = 0.33645 m/s to the left

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