A 70.0 -kg ice hockey goalie, originally at rest, catches a...

A 70.0 -kg ice hockey goalie, originally at rest, catches a 0.150 -kg hockey puck slapped at him at a velocity of 35.0 $\mathrm{ml}$ S. Suppose the goalie and the ice puck have an elastic collision and the puck is reflected back in the direction from which it came. What would their final velocities be in this case?

Key Concepts

Conservation of Momentum

In any collision, the total momentum of the system is conserved provided there is no external impulse. This principle applies to both elastic and inelastic collisions and is used to relate the initial and final velocities of the colliding objects. It is particularly important in multi-body interactions, where the sum of the momenta before the collision equals the sum of the momenta after the collision.

Conservation of Kinetic Energy

In elastic collisions, not only is momentum conserved, but kinetic energy is also conserved. This means that the total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision. This conservation law provides a second equation that, together with momentum conservation, allows for the unique determination of the final velocities of the objects involved.

Relative Velocity in Elastic Collisions

A characteristic of elastic collisions is that the relative speed of separation after the collision equals the relative speed of approach before the collision, but in the opposite direction. This property can be derived from the conservation of kinetic energy and momentum and is useful in simplifying the analysis of the collision. It provides an intuitive and direct way to relate the post-collision velocity differences to the pre-collision conditions.

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