Answer :
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.
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.