A 45.0-kg girl is standing on a 140-kg plank. The plank, originally at rest, is

Question

A 45.0-kg girl is standing on a 140-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 1.31 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

by linear momentum consevation

where mass of girl =MG=45kg , mass of palnk =MP=140kg

velocity of girl relative to the surface of ice= vG

velocity of plank relative to the surface of ice =vP

Given velocity of girl relative to plank =vGP = 1.31 m/s

mass of girl * velocity of girl relative to the surface of ice =mass of plank * velocity of plank relative to the surface of ice

MG vG = MP vP

MG(vGP - vP) =MP vP

vp =MG vGP/(MG + MP) = 45*1.31/(45+140)=0.32 m/s Left

vG = vGP - vP = 1.31 -0.32 = 0.99 m/s

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