Two ice skaters stand at rest in the center of an ice rink....

Two ice skaters stand at rest in the center of an ice rink. When they push off against each other, the $45-\mathrm{kg}$ skater acquires a speed of $0.62 \mathrm{~m} / \mathrm{s}$. If the speed of the other skater is $0.89 \mathrm{~m} / \mathrm{s}$, what is that skater's mass?

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Key Concepts

Momentum

Momentum is a vector quantity defined as the product of an object's mass and velocity. It measures how much motion an object has and is conserved in a closed system, making it a key quantity when analyzing the motion of objects after they interact.

Conservation of Momentum

This principle states that in an isolated system, the total momentum remains constant when no external forces are acting. It is essential in analyzing interactions where objects push off from one another, as the momentum gained by one object must be counterbalanced by the momentum gained by the other in the opposite direction.

Newton's Third Law

Newton's Third Law states that for every action, there is an equal and opposite reaction. In the context of the problem, when one skater applies a force on the other, the other skater applies an equal and opposite force back. This mutual force exchange leads to the conservation of momentum observed in the system.

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