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 calculate the initial momentum of the tennis ball, we can use the formula for momentum, which is given by:

$$ \text{Momentum} = \text{Mass} \times \text{Velocity} $$

Given:
- Initial velocity of the tennis ball = $$ 32 \, \text{m/s} $$
- Mass of the tennis ball = $$ 56 \, \text{g} = 0.056 \, \text{kg} $$

We can calculate the initial momentum of the tennis ball using the formula:

$$ \text{Initial Momentum} = \text{Mass} \times \text{Initial Velocity} $$

Let's calculate the initial momentum of the tennis ball.
Calculate the value by following steps:
- step0: Calculate:
  $$0.056\times 32$$
- step1: Multiply the numbers:
  $$1.792$$
The initial momentum of the tennis ball is $$ 1.792 \, \text{kg m/s} $$.

Now, let's calculate the final momentum of the tennis ball. The final velocity of the tennis ball is given as $$ 58 \, \text{m/s} $$ in the opposite direction. Since the direction is opposite, we need to consider the negative sign for the final velocity.

$$ \text{Final Momentum} = \text{Mass} \times \text{Final Velocity} $$

Let's calculate the final momentum of the tennis ball.
Calculate the value by following steps:
- step0: Calculate:
  $$0.056\left(-58\right)$$
- step1: Multiply the numbers:
  $$-3.248$$
The final momentum of the tennis ball is $$ -3.248 \, \text{kg m/s} $$.

Finally, let's calculate the change in momentum of the tennis ball. The change in momentum is the difference between the final momentum and the initial momentum.

$$ \text{Change in Momentum} = \text{Final Momentum} - \text{Initial Momentum} $$

Let's calculate the change in momentum of the tennis ball.
Calculate the value by following steps:
- step0: Calculate:
  $$-3.248-1.792$$
- step1: Subtract the numbers:
  $$-5.04$$
The change in momentum of the tennis ball is $$ -5.04 \, \text{kg m/s} $$.

Therefore, the initial momentum of the tennis ball is $$ 1.792 \, \text{kg m/s} $$, the final momentum is $$ -3.248 \, \text{kg m/s} $$, and the change in momentum is $$ -5.04 \, \text{kg m/s} $$.
- **Initial Momentum:** $$ 1.792 \, \text{kg m/s} $$ - **Final Momentum:** $$ -3.248 \, \text{kg m/s} $$ - **Change in Momentum:** $$ -5.04 \, \text{kg m/s} $$

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