Final answer:
The question is about conserving momentum during a collision between two pool balls. Using the conservation of momentum, the red pool ball's final velocity is calculated to be 5.83 m/s after a collision with a white pool ball.
Step-by-step explanation:
The question involves a collision between two pool balls and asks for the velocity of one ball after the collision given the masses and velocities before and after the collision. To solve this question, we use the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. Since friction is neglected, this is a closed system where momentum is conserved.
Momentum before collision = Momentum after collision
For the white ball (mass of 1 kg, initial velocity of 10 m/s):
Momentum before = 1 kg × 10 m/s = 10 kg·m/s
For the white ball after the collision (velocity of 3 m/s):
Momentum after = 1 kg × 3 m/s = 3 kg·m/s
Since the red ball was initially at rest, its initial momentum was 0 kg·m/s. To find the velocity of the red ball after the collision, we let V be its final velocity.
For the red ball (mass of 1.2 kg, final velocity V):
Momentum after = 1.2 kg × V = 1.2V kg·m/s
The conservation of momentum equation becomes:
10 kg·m/s = 3 kg·m/s + 1.2 kg × V
Solving for V, the velocity of the red ball after the collision:
V = (10 kg·m/s - 3 kg·m/s) / 1.2 kg = 5.83 m/s
Therefore, the red ball moves with a velocity of 5.83 m/s after the collision.