Question

A 45.0-kg girl is standing on a 150-kg plank. Both are originally at rest on a frozen lake that constitutes a friction-less, flat surface. The girl begins to walk along the plank at a constant velocity of 1.50 m/s relative to the plank. (a) What is the velocity of the plank relative to the ice surface? (b) What is the girl's velocity relative to the ice surface?

Answer 1

The velocity of the plank relative to the ice surface is -67.5 kg·m/s. The girl's velocity relative to the ice surface is 1.50 m/s.

Step-by-step explanation:

To determine the velocity of the plank relative to the ice surface, we can use the principle of conservation of momentum. Since there is no external force acting on the girl and the plank, their total momentum before and after the girl starts walking should be the same.

Before the girl starts walking, the total momentum of the girl and the plank is zero since they are both at rest. After the girl starts walking, her momentum is given by the product of her mass and velocity, which is (45.0 kg)(1.50 m/s) = 67.5 kg·m/s. To keep the total momentum zero, the momentum of the plank must be -67.5 kg·m/s.

Therefore, the velocity of the plank relative to the ice surface is -67.5 kg·m/s.

The girl's velocity relative to the ice surface is the same as her velocity relative to the plank, which is 1.50 m/s, since both the girl and the plank move together.