Final answer:
Using the conservation of momentum, the final momentum of the second particle after the collision can be calculated as -18.4 kg m/s, given that one ends with a momentum of 12.5 kg m/s, and the initial total momentum was -5.9 kg m/s.
Step-by-step explanation:
The student is asking about the conservation of momentum in a two-particle system where both particles are initially moving along the x-axis. One particle has an initial momentum of 15.4 kg m/s (positive direction), and the second particle has an initial momentum of -21.3 kg m/s (negative direction). After the collision, one of the particles has a momentum of 12.5 kg m/s.
To find the final momentum of the other particle, we apply the conservation of momentum principle, which states that the total momentum before the collision is equal to the total momentum after the collision. The initial total momentum is the sum of the individual momenta: 15.4 + (-21.3) = -5.9 kg m/s. With one particle having a momentum of 12.5 kg m/s after the collision, the other must have a momentum that, when combined, equals the initial total momentum.
So, the final momentum of the second particle would be:
Initial total momentum = Final momentum of first particle + Final momentum of second particle
-5.9 = 12.5 + Final momentum of second particle
Final momentum of the second particle = -5.9 - 12.5 = -18.4 kg m/s