Final answer:
The velocity of the target ball after an elastic head-on collision, where the incoming ball of equal mass bounces back, can be calculated using conservation of momentum. The resulting velocity of the target ball is 0.5185 m/s in the same direction as the initial motion of the incoming ball. Therefore, the velocity of the target ball after the collision is 0.5185 m/s in the same direction as the initial motion of the incoming ball.
Step-by-step explanation:
To calculate the velocity of the target ball after the collision, we apply the conservation of momentum and the fact that the collision is elastic. In an elastic collision, both momentum and kinetic energy are conserved. Because the balls have equal mass and the incoming ball bounces back with a different speed, the target ball will move with the difference in velocity between the initial and final velocities of the incoming ball.
The momentum before the collision is given by:
Initial momentum = mass of incoming ball × its initial velocity = 0.305 kg × 5.6 m/s.
After the collision, the incoming ball has a momentum of:
Final momentum of incoming ball = - (mass of incoming ball × its final velocity) = - (0.305 kg × 3.9 m/s),
where the negative sign indicates the incoming ball has reversed direction.
To find the final velocity of the target ball, we set the total initial momentum equal to the total final momentum (considering that the target ball was initially at rest):
Initial momentum = Final momentum of the incoming ball + (mass of target ball × final velocity of target ball)
Since the masses are the same and the target ball starts at rest, we can solve for the final velocity of the target ball as:
Final velocity of target ball = (Initial momentum + Final momentum of incoming ball) / mass of target ball
Using the numbers, we calculate:
Final velocity of target ball = (0.305 kg × 5.6 m/s - 0.305 kg × 3.9 m/s) / 0.305 kg
Final velocity of target ball = (1.708 - 1.1895) m/s
Final velocity of target ball = 0.5185 m/s
Therefore, the velocity of the target ball after the collision is 0.5185 m/s in the same direction as the initial motion of the incoming ball.