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Answer :
Final answer:
To find the velocity of the second car after an elastic collision, apply conservation of momentum. Using the given and reversed velocities of the first car, along with their masses, solve for the unknown velocity of the second car. The collision is elastic, as kinetic energy is conserved.
Explanation:
To determine the velocity of the second vehicle after an elastic collision, we use the conservation of momentum and the fact that kinetic energy is conserved in an elastic collision. Given that the 96-kg bumper car reverses direction and moves with a velocity of -0.209 m/s (note that the velocity provided in the question seems to be a typo, as a velocity of -209 m/s is unrealistic), we can set up the following equations:
Momentum before collision = Momentum after collision:
(96 kg × 1.24 m/s) + (135 kg × 0 m/s) = (96 kg × -0.209 m/s) + (135 kg × v)
Kinetic Energy before collision = Kinetic Energy after collision (not used in this calculation but is a condition for an elastic collision).
Solving the momentum equation for v gives us the velocity of the second bumper car. The type of collision is elastic, as the question states that the bumper cars "bounce elastically" meaning no kinetic energy is lost.
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