What is the velocity of the girl relative to the ice surface and the velocity of the plank relative to the ice surface in the following case:A 32.6 kg girl is standing on a 230 kg plank.  The...

What is the velocity of the girl relative to the ice surface and the velocity of the plank relative to the ice surface in the following case:

A 32.6 kg girl is standing on a 230 kg plank.  The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless supporting surface.  The girl begins to walk along the plank at a constant speed of 1.83 m/s to the right relative to the plank.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A 32.6 kg girl is standing on a 230 kg plank.  The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless supporting surface.  The girl begins to walk along the plank at a constant speed of 1.83 m/s to the right relative to the plank.

As there is no force of friction between the plank and the ice that it rests on, the law of conservation of momentum plays a role making the plank move in a direction opposite to that in which the girl is moving. The mass of the girl is 32.6 kg and she is moving at 1.83 m/s to the right. The momentum of the girl is 32.6*1.83 = 59.658 kg*m/s . The mass of the plank is 230 kg. It moves in an opposite direction with a magnitude equal to 59.658/230 = 0.2593 m/s. The plank moves towards the left at 0.2593 m/s.

The velocity of the girl relative to the ice surface is 1.83 - 0.2593 = 1.5706 m/s to the right. The velocity of the plank relative to the ice surface is 0.2593 m/s towards the left.

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