Question

Bumper car A (281 kg) moving +2.82 m/s makes an elastic collision with bumper car B (209 kg) moving -1.72 m/s. What is the velocity of car B after the collision?

Answer 1

The student is asked to calculate the final velocity of car B after an elastic collision with car A, using the principles of conservation of momentum and kinetic energy. The masses and initial velocities of both cars are given, and the final velocity of car B can be determined by solving the system of equations derived from the conservation laws.

Step-by-step explanation:

The question involves a calculation of velocities after an elastic collision between two bumper cars with different masses. The law of conservation of momentum and kinetic energy are key in solving these type of physics problems. We can use the conservation equations for elastic collisions to determine the final velocity of car B (v2') after impact:

Conservation of momentum: m1v1 + m2v2 = m1v1' + m2v2',
where m1 and m2 are the masses of cars A and B, and v1, v2, v1', and v2' are the initial and final velocities of cars A and B respectively.

Conservation of kinetic energy: 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2 = 0.5 * m1 * v1'^2 + 0.5 * m2 * v2'^2.

However, since the question provides specific masses and velocities, we would insert those values into the equations to solve for car B's final velocity (v2'). The difficulty lies in solving this system of equations which involves algebraic manipulation.