Final answer:
The total momentum of the system after the collision is 0.19 kg-m/s south. We used the principle of conservation of momentum which states the total momentum remains constant in the absence of external forces. The correct answer is option: B. 0.19 kg m/s south.
Step-by-step explanation:
To determine the momentum of the system after the collision between the two billiard balls, we will use the principle of conservation of momentum. This principle states that the total momentum of a closed system remains constant if no external forces act on it. In this case, we are dealing with an isolated system of two billiard balls colliding.
Before the collision, we have one billiard ball moving north and the other moving south. The momentum of each ball can be calculated by multiplying the mass of the ball by its velocity.
For the ball moving north:
- Momentum = Mass x Velocity = 0.21 kg x 1.7 m/s = 0.357 kg·m/s north
For the ball moving south:
- Momentum = Mass x Velocity = 0.21 kg x -2.6 m/s = -0.546 kg·m/s (since south is the opposite direction, it is negative)
Adding these two momenta together gives us the total momentum of the system before the collision:
Total momentum before = 0.357 kg·m/s + (-0.546 kg·m/s) = -0.189 kg·m/s
Since there are no external forces, the total momentum of the system after the collision will be the same as before the collision, but the direction will depend on the sign of the momentum.
The negative value indicates that the total momentum is in the south direction, so the correct answer is: B. 0.19 kg·m/s south