Chapter 1.8, Problem 68PS

Solution

To calculate: How long the defensive player’s teammates have intercept the ball before it hits the ground if the player bats the ball downward at an initial vertical velocity of $-50$ feet per second when the ball is 7 feet above the ground.

The ball was in the air for about 0.134 seconds.

Given information:

The values are $h=0,v_0=-50,\text{and}{h}_0=7$ .

Formula used:

Use the quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ .

Calculation:

Write the height model:

  $h=-16t^2+v_{0}t+h_0$

Substitute the values of $h=0,v_0=-50,\text{and}{h}_0=7$ ,

  $\begin{array}{c}0=-16t^2+\left(-50\right)t+7\\ 0=16t^2-50t+7\end{array}$

Apply the quadratic formula,

  $\begin{array}{c}t=\frac{-\left(-50\right)\pm \sqrt{{\left(-50\right)}^2-4\left(16\right)\left(7\right)}}{2\left(-16\right)}\\ t=\frac{50\pm \sqrt{2948}}{-32}\\ t\approx -3.26ort\approx 0.134\end{array}$

Therefore, the ball is in the air for about 0.134 seconds.