Final answer:
The mass of the tennis ball can be determined by applying the conservation of momentum principle, specifically focusing on horizontal momentum before and after the collision between the racquet and the ball.
Step-by-step explanation:
The student wants to know the mass of a tennis ball based on a scenario provided. Since no external forces act on the racquet and ball system and the ball is hit at the peak of its trajectory, the problem can be approached using momentum conservation principles. For illustration, if we were using data such as a racquet exerting a force of 540 N for 5.00 ms giving the ball a final velocity of 45.0 m/s, we would use the impulse-momentum theorem which tells us that impulse is equal to the change in momentum of the object. The impulse here is the force times the time of contact, and the change in momentum would be the final momentum minus the initial momentum, with the initial momentum being zero since the ball starts from rest. By knowing the impulse and the final velocity, we could solve for the mass of the tennis ball.
To solve for the mass of the tennis ball in the student's actual problem, we set the initial horizontal momentum of the racquet (which is mass of the racquet times its initial velocity before hitting the ball) equal to the final horizontal momentum of both the racquet and the tennis ball after the collision. This setup is based on the conservation of horizontal momentum. The racquet's horizontal momentum before collision is zero since it is moving vertically, so we only consider its mass and the velocity after collision (350 g × 25 m/s). The final momentum is the sum of the racquet's and ball's momenta after the collision. Given the common velocity after impact (25 m/s), we can algebraically solve for the tennis ball's mass.