Chapter 9, Problem 25MCQ

To determine

Find how many seconds it will take for the ball to reach the bottom of the pole.

Answer to Problem 25MCQ

6.83 seconds it will take for the ball to reach the bottom of the pole.

Explanation of Solution

Given:

Della`s parents are throwing a sweet 16 party for her. At 10:00, a ball will slide 25 feet down a pole and light up. A function that models the drop is $h=-t^2+5t+25$ , where h is height in feet of the ball after t seconds.

Concept Used:

The equation: $h=-t^2+5t+25$

The moment the ball reaches the bottom of the pole when h = 0

Rewrite the equation when h = 0.

  $\begin{array}{l}h=-t^2+5t+25\\ 0=-t^2+5t+25\\ -t^2+5t+25=0\end{array}$

Calculation:

Solve for t by using the quadratic formula: $-t^2+5t+25=0$

  $\begin{array}{l}a{x}^2+bx+c=0,\text{then}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ -t^2+5t+25=0[\text{make}\text{right}\text{side}\text{equal}\text{to}\text{0}]\\ a=-1;b=5;c=25\\ t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ t=\frac{-5\pm \sqrt{{(5)}^2-4·-1·25}}{2·-1}=\frac{-5\pm \sqrt{25+100}}{-2}=\frac{-5\pm \sqrt{125}}{-2}=\frac{-5\pm 5\sqrt{3}}{-2}\\ t=\frac{-5-5\sqrt{3}}{-2}\text{and}\frac{-5+5\sqrt{3}}{-2}\\ t=6.83\text{and}-1.83\\ t=6.83\text{seconds}\end{array}$

Time cannot be negative.

6.83 seconds it will take for the ball to reach the bottom of the pole.

Thus, 6.83 seconds it will take for the ball to reach the bottom of the pole.