4. Then a tennis ployer's racquet mukes contace with an approaching tennis ball, the sperd of che tennis ball changes from an inicial velociry of \( 32 \mathrm{~m} \mathrm{~s}^{-1} \) towands the racquer, to a velocity of \( 58 \mathrm{~ms}^{-1} \) in the opporite diection. The mase of the tenais ball is 56 g 2. Calculate the initial momentum of the tennis ball. 1. Cilculate the final momentum of the teanis ball c. Calculate the change in momentum of the tennis lall.
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To get started, let's tackle the momentum calculations. The initial momentum of the tennis ball can be calculated using the formula \( \text{momentum} = \text{mass} \times \text{velocity} \). The mass in kilograms is \( 0.056 \, \text{kg} \), and the initial velocity is \( -32 \, \text{m/s} \) (negative because it's approaching the racquet): \[ \text{Initial momentum} = 0.056 \, \text{kg} \times (-32 \, \text{m/s}) = -1.792 \, \text{kg m/s}. \] For the final momentum, we have: \[ \text{Final momentum} = 0.056 \, \text{kg} \times 58 \, \text{m/s} = 3.248 \, \text{kg m/s}. \] Now, let's find the change in momentum: \[ \text{Change in momentum} = \text{Final momentum} - \text{Initial momentum} = 3.248 \, \text{kg m/s} - (-1.792 \, \text{kg m/s}) = 5.04 \, \text{kg m/s}. \] So, the tennis ball’s change in momentum is \( 5.04 \, \text{kg m/s} \)! --- In the tennis universe, momentum is like the invisible scorekeeper! When the racquet makes contact with the ball, it alters not just the ball's path but its energy and speed too. It's a thrilling dance of physics in action, every swing translating momentum into potential victories on the court! And let's not forget the practical aspects of these calculations! Tennis players use these principles intuitively. For example, understanding how to swing for maximum impact can help them better control their shots, leading to improved gameplay strategies. So next time you're on the court, remember: each swing is a lesson in physics!
