Final answer:
In an elastic collision, two equal-mass bumper cars will swap speeds. The car initially behind with a speed of 6.00 m/s will slow down to 5.60 m/s, and the car in front initially at 5.60 m/s will speed up to 6.00 m/s after the collision.
Step-by-step explanation:
In an elastic collision between two objects of equal mass, where one object is moving and the other is at rest or moving in the same direction, the two objects will swap velocities if the collision is perfectly elastic. We use the principles of conservation of momentum and conservation of kinetic energy to solve such problems.
To find the final speeds of the bumper cars, use the following equations:
- Conservation of momentum: m1⋅v1_initial + m2⋅v2_initial = m1⋅v1_final + m2⋅v2_final
- Conservation of kinetic energy: 0.5⋅m1⋅v1_initial^2 + 0.5⋅m2⋅v2_initial^2 = 0.5⋅m1⋅v1_final^2 + 0.5⋅m2⋅v2_final^2
For our scenario:
- m1 = m2 = 400 kg
- v1_initial = 5.60 m/s
- v2_initial = 6.00 m/s
After some algebraic manipulation, the final speeds are found to be:
- v1_final = 6.00 m/s
- v2_final = 5.60 m/s
Therefore, the correct answer is: (c) 6.00 m/s, 5.60 m/s.