Question

A 45.6-kg girl is standing on a 159-kg plank. Both originally at rest on a frozen...

A 45.6-kg girl is standing on a 159-kg plank. Both originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity of 1.46î m/s relative to the plank.

(a) What is the velocity of the plank relative to the ice surface? î m/s

(b) What is the girl's velocity relative to the ice surface? î m/s

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Answer #1

Mass of the girl = m1 = 45.6 kg

Mass of the plank = m2 = 159 kg

Velocity of the girl relative to the ice surface = V1

Velocity of the plank relative to the ice surface = V2

Velocity of the girl relative to the plank = V12 = 1.46 i m/s

V12 = V1 - V2

1.46 = V1 - V2

V1 = 1.46 + V2

There is no external force acting on the system hence the momentum of the system remains constant.

Initially the system is at rest hence the initial momentum if the system is zero.

m1V1 + m2V2 = 0

(45.6)(1.46 + V2) + (159)V2 = 0

V2 = -0.325 i m/s

V1 = 1.46 + V2

V1 = 1.46 + (-0.325)

V1 = 1.135 i m/s

a) Velocity of the plank relative to the ice surface = -0.325 i m/s

b) Velocity of the girl relative to the ice surface = 1.135 i m/s

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