Chapter 9, Problem 7TP

Solution

To determine the initial velocity does second person have to kick the ball.

The initial velocity is $45.70\text{ feet}$ per second for second person to kick the ball.

Given:

The first person kicks a soccer ball at an angle of ${45}^{°}$ with an initial velocity $40\text{ feet}$ per second.

Calculation:

The horizontal distance $d$ is given by:

  $\begin{array}{l}d=\frac{v^2}{32}\sin 2\theta \\ d=\frac{{\left(40\right)}^2}{32}\sin 2\left({45}^{°}\right)\\ d=\frac{1600}{32}\sin {90}^{°}\\ d=50\times 1\\ d=50\text{ feet}\end{array}$

Now, the second person kick the ball at an angle of ${25}^{°}$ with the same horizontal distance of $d=50\text{ feet,}$ so the initial velocity for him is given as:

  $\begin{array}{l}d=\frac{v^2}{32}\sin 2\theta \\ v^2=\frac{50\times 32}{\sin 2\left({25}^{°}\right)}\\ v^2=\frac{1600}{\sin {50}^{°}}\\ v^2=\frac{1600}{0.766}\\ v^2=2088.77\\ v=\sqrt{2088.77}\\ v=45.70\text{ feet per second}\end{array}$

Hence the initial velocity for second person should be $45.70\text{ feet per socond}\text{.}$