A 45.0 -kg girl is standing on a 150 -kg plank. Both are...

A 45.0 -kg girl is standing on a 150 -kg plank. Both are 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 $1.50 \mathbf{i} \mathrm{m} / \mathrm{s}$ 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?

Key Concepts

Reference Frames

A reference frame is a viewpoint from which motion is observed and measured. In this scenario, the plank is moving relative to the ice and the girl is moving relative to the plank. Recognizing the appropriate reference frame allows one to correctly apply conservation laws and properly combine velocities.

Center of Mass

The center of mass of a system is the point where the total mass of the system can be considered to be concentrated. For systems with no external forces, the center of mass does not accelerate. In the girl's and plank's system, the center of mass remains stationary, which is an insight that can help in determining the relationship between the velocities of the girl and the plank.

Relative Velocity

Relative velocity is the rate at which one object moves with respect to another. The problem involves the girl’s speed relative to the plank and asks for the velocity of both the plank and the girl relative to the ice surface. Understanding how to add or subtract velocities based on different reference frames is crucial to solving such problems.

Conservation of Momentum

This concept states that in an isolated system where no external forces are acting, the total momentum remains constant. In the given problem, since the ice surface is frictionless, there are no external horizontal forces acting on the system of the girl and the plank, which means any momentum gained by one must be balanced by the momentum of the other.

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