Two identical hockey pucks are moving on a hockey rink at...

Two identical hockey pucks are moving on a hockey rink at the same speed of $3 \mathrm{~m} / \mathrm{s}$ and in perpendicular directions when they strike each other as shown. Assuming a coefficient of restitution $e=0.9,$ determine the magnitude and direction of the velocity of each puck after impact.

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Key Concepts

Coefficient of Restitution

This concept describes the ratio of relative speeds after and before a collision along the line of impact. It quantifies how 'elastic' a collision is and determines the amount of kinetic energy preserved in the normal direction after the collision, with a value of 1 representing a perfectly elastic collision and values less than 1 indicating inelastic behavior.

Conservation of Momentum

In the absence of external forces, the total momentum of a system is conserved during a collision. This principle is used to relate the velocities of colliding bodies before and after impact by applying momentum conservation separately to each independent (typically orthogonal) direction.

Vector Decomposition in Collision Analysis

When dealing with collisions occurring at angles, it is essential to break velocity vectors into components along the normal (line of collision) and tangential directions. This decomposition allows one to apply the coefficient of restitution to the normal components while recognizing that the tangential components remain unchanged, facilitating the analysis of the overall post-collision velocities.

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