Two figure skaters are coasting in the same direction, with...

Two figure skaters are coasting in the same direction, with the leading skater moving at $5.5 \mathrm{m} / \mathrm{s}$ and the trailing skating moving at $6.2 \mathrm{m} / \mathrm{s}$. When the trailing skater catches up with the leading skater, he picks her up without applying any horizontal forces on his skates. If the trailing skater is 50\% heavier than the 50-kg leading skater, what is their speed after he picks her up?

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Key Concepts

Conservation of Momentum

This principle states that in an isolated system with no external forces, the total momentum before an event is equal to the total momentum after the event. In collisions or interactions where external influences are negligible, momentum is redistributed among the objects involved, but the overall momentum remains constant. This concept is crucial in solving problems involving objects interacting, such as coupled movements or collisions, where determining the final speed or outcome requires accounting for the contributions of all masses and velocities involved.

Inelastic Collision

An inelastic collision is one in which the colliding objects stick together or move as a single entity after impact. While kinetic energy is not conserved in such collisions due to energy transformation into other forms like heat or sound, the total momentum remains conserved. This concept is particularly important when analyzing scenarios where objects combine their motion post-collision, requiring the use of conservation of momentum to determine the resulting velocity of the combined mass.

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