To determine the total momentum of the carts after the collision, we need to use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision in a closed system, assuming no external forces act on the system.
Firstly, let's identify the given momenta of the two carts before the collision:
- Cart 1 had a momentum of [tex]\(-6 \, \text{kg} \cdot \text{m/s}\)[/tex].
- Cart 2 had a momentum of [tex]\(10 \, \text{kg} \cdot \text{m/s}\)[/tex].
We calculate the total momentum before the collision by summing the individual momenta of the two carts:
[tex]\[
\text{Total momentum before collision} = \text{momentum of Cart 1} + \text{momentum of Cart 2}
\][/tex]
Substituting the given values:
[tex]\[
\text{Total momentum before collision} = -6 \, \text{kg} \cdot \text{m/s} + 10 \, \text{kg} \cdot \text{m/s}
\][/tex]
Perform the addition:
[tex]\[
\text{Total momentum before collision} = 4 \, \text{kg} \cdot \text{m/s}
\][/tex]
According to the conservation of momentum, the total momentum after the collision will be equal to the total momentum before the collision. Therefore:
[tex]\[
\text{Total momentum after the collision} = 4 \, \text{kg} \cdot \text{m/s}
\][/tex]
Thus, the total momentum of the carts after the collision is:
[tex]\[
4 \, \text{kg} \cdot \text{m/s}
\][/tex]
The correct answer to the question is:
[tex]\[
4 \, \text{kg} \cdot \text{m/s}
\][/tex]
