91影视

Given in the question

Mass of the tennis ball$m=57\mathrm{g}=57脳{10}^{-3}\mathrm{kg}$

Velocity of the served ball$v_2=73.14\mathrm{m}/\mathrm{s}$

Time of contact$鈭�t=30\mathrm{ms}$

The momentum of a particle: The momentum $\stackrel{\mathbf{鈫�}}{\mathbf{P}}$of a particle is a vector quantity equal to the product ofthe particle鈥檚 mass mand velocity $\stackrel{\mathbf{鈫�}}{\mathbf{v}}$.

$\stackrel{\mathbf{鈫�}}{\mathbf{p}}\mathbf{=}\mathit{m}\stackrel{\mathbf{鈫�}}{\mathbf{v}}$

Newton鈥檚second law says that the net force on a particleis equal to the rate of change of the particle鈥檚momentum.

$\underset{\mathbf{}}{\mathbf{鈭�}}\mathit{F}\mathbf{=}\frac{\mathbf{d}\mathbf{p}}{\mathbf{d}\mathbf{t}}$

Impulse and momentum theorem

If $\stackrel{\mathbf{鈫�}}{\mathbf{J}}$is impulse and $\stackrel{\mathbf{鈫�}}{{\mathbf{P}}_{\mathbf{1}}}$is initial momentum and$\stackrel{\mathbf{鈫�}}{{\mathbf{P}}_{\mathbf{2}}}$ is final momentum

Then

$\stackrel{\mathbf{鈫�}}{\mathbf{J}}\mathbf{=}{\stackrel{\mathbf{鈫�}}{\mathbf{P}}}_{\mathbf{2}}\mathbf{-}\stackrel{\mathbf{鈫�}}{{\mathbf{P}}_{\mathbf{1}}}$

Given in the question

$$\begin{gathered} m=57\mathrm{g}=57脳{10}^{-3}\mathrm{kg} \\ {\mathrm{v}}_2=73.14\mathrm{m}/\mathrm{s} \\ 鈭�\mathrm{t}=30\mathrm{ms} \end{gathered}$$

As we know that service means hitting the ball and starting the play, since the ball is initially at rest so initial momentum is zero.

$p_1=0$

Final momentum

$$\begin{gathered} p_2=m{v}_2 \\ =\left(57脳{10}^{-3}\mathrm{kg}\right)\left(73.14\mathrm{m}/\mathrm{s}\right) \\ =4.17\mathrm{kg}.\mathrm{m}/\mathrm{s} \end{gathered}$$

From impulse momentum theorem.

$$\begin{gathered} \stackrel{鈫�}{J}=\stackrel{鈫�}{P_2}-\stackrel{鈫�}{P_1} \\ =4.17\mathrm{kg}.\mathrm{m}/\mathrm{s}-0 \\ =4.17\mathrm{kg}.\mathrm{m}/\mathrm{s} \end{gathered}$$

The impulse exerted by Big Bill on the tennis ball in his record serve is 4.17kg.m/s

From Newton鈥檚 second law

$$\begin{gathered} \underset{}{鈭�}F=\frac{dp}{dt} \\ \underset{}{鈭�}F=\frac{p_2-p_1}{鈭�t} \\ =\frac{4.17\mathrm{kg}.\mathrm{m}/\mathrm{s}-0}{30脳{10}^{-3}\mathrm{s}} \\ =138.97\mathrm{N} \end{gathered}$$

The force exerted by Big Bill on the tennis ball in his record serve is 138.97 N.

Given in the question

$m=57\mathrm{g}=57脳{10}^{-3}\mathrm{kg}$

Considering the direction from bill to his opponent is a positive direction.

$$\begin{gathered} {\mathrm{v}}_2=-55.0\mathrm{m}/\mathrm{s} \\ 鈭�\mathrm{t}=30\mathrm{ms} \end{gathered}$$

After Big Bill serves the ball momentum of the ball is

$p_1=4.17\mathrm{kg}.\mathrm{m}/\mathrm{s}$

Final momentum

$$\begin{gathered} p_2={\mathrm{mv}}_2 \\ =\left(57脳{10}^{-3}\mathrm{kg}\right)\left(-55\mathrm{m}/\mathrm{s}\right) \\ =-3.135\mathrm{kg}.\mathrm{m}/\mathrm{s} \end{gathered}$$

From impulse momentum theorem.

$$\begin{gathered} \stackrel{鈫�}{J}=\stackrel{鈫�}{P_2}-\stackrel{鈫�}{P_1} \\ =-3.135\mathrm{kg}.\mathrm{m}/\mathrm{s}-4.17\mathrm{kg}.\mathrm{m}/\mathrm{s} \\ =-7.3\mathrm{kg}.\mathrm{m}/\mathrm{s} \end{gathered}$$

The impulse exerted by the opponent is -7.3kg.m/s

From Newton鈥檚 second law

$$\begin{gathered} \underset{}{鈭�}F=\frac{dp}{dt} \\ \underset{}{鈭�}F=\frac{{\mathrm{p}}_2-{\mathrm{p}}_1}{鈭�\mathrm{t}} \\ =\frac{-3.135\mathrm{kg}.\mathrm{m}/\mathrm{s}-4.17\mathrm{kg}.\mathrm{m}/\mathrm{s}}{30脳{10}^{-3}\mathrm{s}} \\ =-243.5\mathrm{N} \end{gathered}$$

The force exerted by the opponents -243.5 N.