Final answer:
The speed of the tennis ball after the collision is found using the conservation of momentum and is calculated to be 15 m/s East. Hence, option (b) is correct.
Step-by-step explanation:
To find the speed and direction of the tennis ball after the collision, we can apply the conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. The momentum of the bowling ball and tennis ball before the collision can be calculated as follows:
- Initial momentum of the bowling ball = mass × velocity = 10 kg × 5.00 m/s = 50 kg·m/s East
- Initial momentum of the tennis ball = mass × velocity = 0.10 kg × 5.00 m/s = 0.5 kg·m/s West (which can be considered as -0.5 kg·m/s East for calculation purposes)
Thus, total initial momentum = 50 kg·m/s East - 0.5 kg·m/s East = 49.5 kg·m/s East.
After the collision, the bowling ball's momentum will be 10 kg × 4.80 m/s = 48 kg·m/s East. To find the final momentum of the tennis ball, we subtract the bowling ball's final momentum from the total initial momentum:
- Total final momentum = Initial total momentum - Final momentum of bowling ball
- Final momentum of the tennis ball = 49.5 kg·m/s East - 48 kg·m/s East = 1.5 kg·m/s East
To find the final velocity of the tennis ball, we divide its final momentum by its mass:
- Final velocity of the tennis ball = Final momentum of tennis ball / mass of tennis ball
- Final velocity of the tennis ball = 1.5 kg·m/s East / 0.10 kg = 15 m/s East
Therefore, the correct answer is 15 m/s East (Option b).