Question 7. A 45.0-kg girl is standing on a 169-kg plank. The plank, originally

Question

Question 7.

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 1.35 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?

(b) What is the velocity of the plank relative to the surface of ice?

Explanation / Answer

For every action there is an equal and opposite reaction.

If the girls exerts a force on the plank to accellearate her to 1.55 m/s then she also pushes the board backward on the ice.

I'm going to use kg in this calculation since any conversion to Newtons will only be cancelled out.

45 kg * 1.55 m/s = 69.75 kg * m/s

The board must have the same energy,

69.75 kg * m/s = 162 kg * Velocity of the board

solving the the above equation the velocity of the board is
0.431 m/s

Since the board is traveling backward as the girl is traveling forward, her speed relative to the ice is 1.55 m/s - 0.431 m/s =1.12 m/s

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