Chapter 3, Problem 72GP

(a)

To determine

The distance covered by the ball without catching.

Answer to Problem 72GP

The distance covered by the ball without being caught is $67.33\text{m}$ .

Explanation of Solution

Given info:

The height of the ball above the ground is, $h=0.90\text{m}$ .

The angle of the ball is, $\theta =61°$ .

The initial speed of the ball is, $u=28\text{m}/\text{s}$ .

Formula Used:

The expression to calculate the time in which the ball falls on the ground is,

  $h=ut\sin \theta -\frac{1}{2}g{t}^2$

The expression to calculate the distance covered by the ball without being caught is,

  $x=ut\cos \theta$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{l}0.9\text{m}=\left(28\text{m}/\text{s}\right)\left(\sin 61°\right)t-\frac{1}{2}\left(9.8\text{m}/{\text{s}}^2\right)t^2\\ \left(4.9\text{m}/{\text{s}}^2\right)t^2-\left(24.49\text{m}/\text{s}\right)t+0.9\text{m}=0\\ t=4.96\text{s}\end{array}$

Substitute all the values in the above expression.

  $\begin{array}{c}x=\left(28\text{m}/\text{s}\right)\left(\cos 61°\right)\left(4.96\text{s}\right)\\ =67.33\text{m}\end{array}$

Conclusion:

Thus, the distance covered by the ball without being caught is $67.33\text{m}$ .

(b)

To determine

The speed of the centerfielder.

Answer to Problem 72GP

The speed of the center fielder is $7.59\text{m}/\text{s}$ .

Explanation of Solution

Given info:

The distance of the centerfielder from home plate is, $X=105\text{m}$ .

Formula Used:

The expression to calculate the speed of the center fielder is,

  $v=\frac{X-x}{t}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}v=\frac{105\text{m}-67.33\text{m}}{4.96\text{s}}\\ =7.59\text{m}/\text{s}\end{array}$

Conclusion:

Thus, the speed of the center fielder is $7.59\text{m}/\text{s}$ .