Final answer:
Using the law of conservation of momentum, the velocity of the blue bumper car after the collision can be calculated to be 3.5 m/s to the right, assuming no external forces such as friction are involved in the collision and that the cars do not stick together.
Step-by-step explanation:
The red bumper car has a mass of 7 kg and an initial velocity of 8 m/s, while the blue bumper car has a mass of 16 kg and is initially stationary. After the collision, the red bumper car comes to a stop, which means its final velocity is 0 m/s. Given that the only two objects interacting are the two bumper cars and there are no other external forces (friction is ignored), the initial momentum can be calculated as:
- Initial momentum of red car = mass × velocity = 7 kg × 8 m/s = 56 kg·m/s (to the right).
- Initial momentum of blue car = 16 kg × 0 m/s = 0 kg·m/s (since it's stationary).
Therefore, the total initial momentum of the system is 56 kg·m/s to the right. After the collision, the red car's momentum is 0 kg·m/s (since it's not moving), and because momentum is conserved, the blue car must now have a momentum of 56 kg·m/s to the right. We can calculate the blue car's velocity after the collision:
- Final momentum of blue car = mass × velocity = 16 kg × velocity
- 56 kg·m/s = 16 kg × velocity
- Velocity of blue car = 56 kg·m/s ÷ 16 kg = 3.5 m/s to the right.
So, the velocity of the blue bumper car after the collision is 3.5 m/s to the right.