A 45.0-kg girl is standing on a 157-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 1.56 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 the ice?

In physics, the girl's motion relative to the ice can be found using the concept of conservation of momentum. Initially, both the plank and the girl were at rest, so their total momentum was zero. When the girl walks with a velocity of 1.56 m/s on the plank, to conserve momentum of the system, the plank moves in the opposite direction.

We calculate the velocity of the plank due to the girl's movement with the following equation: (mass of girl * velocity of girl) = (mass of plank * velocity of plank). Therefore, the velocity of the plank is (45.0kg * 1.56m/s) / 157kg = -0.448m/s (negative sign indicates direction opposite to the girl's movement).

Now, to find the girl's velocity relative to the ice, we add the girl's velocity with respect to the plank and plank's velocity with respect to the ice. Thus, the girl's velocity with respect to ice is 1.56 m/s - 0.448 m/s = 1.112 m/s.

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