A 222 kg bumper car moving to the right at [tex]3.10 \, \text{m/s}[/tex] collides with a 165 kg bumper car moving to the left at [tex]1.88 \, \text{m/s}[/tex]. Find the total momentum of the system.

To find the total momentum of the system, we use the principle of conservation of momentum. Momentum is calculated as the product of mass and velocity.

Here are the steps involved:

1. Identify the masses and velocities of the bumper cars:
- The first bumper car has a mass of 222 kg and is moving to the right at a velocity of 3.10 m/s.
- The second bumper car has a mass of 165 kg and is moving to the left at a velocity of 1.88 m/s. Since it's moving to the left, this velocity is negative.

2. Calculate the momentum of each bumper car:
- Momentum is given by the formula: momentum = mass × velocity.

- For the first bumper car:
[tex]\[
\text{Momentum of car 1} = 222 \, \text{kg} \times 3.10 \, \text{m/s} = 688.2 \, \text{kg} \cdot \text{m/s}
\][/tex]

- For the second bumper car:
[tex]\[
\text{Momentum of car 2} = 165 \, \text{kg} \times (-1.88 \, \text{m/s}) = -310.2 \, \text{kg} \cdot \text{m/s}
\][/tex]

3. Calculate the total momentum of the system:
- Add the momentum of both bumper cars to find the total momentum.
[tex]\[
\text{Total momentum} = 688.2 \, \text{kg} \cdot \text{m/s} + (-310.2 \, \text{kg} \cdot \text{m/s}) = 378 \, \text{kg} \cdot \text{m/s}
\][/tex]

Therefore, the total momentum of the system is 378 kg·m/s.