Final answer:
Using conservation of momentum and conservation of kinetic energy, we can calculate the final velocities of two pucks after an elastic collision, and we can also confirm whether the collision was elastic by comparing total kinetic energy before and after. The mass and velocity contribute to the outcome of the collision.
Step-by-step explanation:
When two pucks collide on an air table and one of them is initially at rest, the principle of conservation of momentum and conservation of energy are applicable if the collision is elastic. These two conservation laws allow us to set up two equations: one for momentum and one for kinetic energy. The final velocities of the pucks can be calculated using these laws taking into account the mass and initial velocities of the pucks. To verify that the collision is elastic, one must confirm that the total kinetic energy before and after the collision remains constant. For example, if a stationary red puck with a mass of 15 g is hit by a blue puck with a mass of 15 g moving at 2.5 m/s, and after the collision, the red puck is moving at 2.5 m/s, the blue puck must be at rest to conserve momentum, as the momentum before and after the collision is the same, and the total kinetic energy is also conserved. In the case of the goalie and the puck, their final velocities can be determined by the same principles. The mass and velocity of each object affect the outcomes of the collision, with mass being directly proportional and velocity being squared in terms of its contribution to kinetic energy.