Chapter 9.6, Problem 16P

A basketball is passed through the air. The height $h$ of the ball in the feet after the distance $d$ in feet the ball travels horizontally is given by $h=-d^2+10d+5.$

How far horizontally from the player passing the ball land on the ground?

To determine

To find : How far horizontally from the player passing the ball will the ball land on the ground.

Answer to Problem 16P

The ball land 10.4 feet far from the player passing the ball.

Explanation of Solution

Given information :

The height h of the bal in feet after the distance d in feet the ball travels horizontally is given by $h=-d^2+10d+5$ .

Calculation :

When the ball land on the ground then the height becomes zero that is $h=0$ .

Therefore, set the equation to zero and solve for d:

  $-d^2+10d+5=0$

This is a quadratic equation.

For the quadratic equation

  $a{x}^2+bx+c=0$ the quadratic formula is

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Now, for the given equation

  $-d^2+10d+5=0$

  $a=-1$ ,

  $b=10$ and $c=5$ .

Therefore,

  $\begin{array}{l}d=\frac{-10\pm \sqrt{{\left(10\right)}^2-4\left(-1\right)\left(5\right)}}{2\left(-1\right)}\\ d=\frac{-10\pm \sqrt{100+20}}{-2}\\ d=\frac{-10\pm \sqrt{120}}{-2}\\ d=\frac{-10\pm 2\sqrt{30}}{-2}\\ d=5\mp \sqrt{30}\\ d=5-\sqrt{30}\mathrm{and}d=5+\sqrt{30}\\ d=-0.48\text{ and }d=10.4\end{array}$

Since, distance can never be negative, therefore

  $d=10.4$

Hence,

The ball land 10.4 feet far from the player passing the ball.