Chapter 9.5, Problem 28PPS

To determine

Approximately find the rider to drop from 60 feet to zero feet.

Answer to Problem 28PPS

It takes 2.5 seconds for the rider to drop from 60 feet to zero feet.

Explanation of Solution

Given:

The Demon Drop at Cedar point in Ohio takes to the top of a tower and drops them 60 feet. A function that approximates this ride is , where h is the height in feet and t is the time in seconds. About how many seconds does it take for riders to drop from 60 feet to 0 feet?

Concept Used:

The quadratic equation: $h=-16t^2+64t-60$

To find the time for the rider to drop from 60 feet to zero feet, substitute: $h=0$

Calculation:

The quadratic equation: $h=-16t^2+64t-60$

To find the time for the ball in the air, substitute: $h=0$

Rewrite the equation: $-16t^2+64t-60=0$ solve for tine (t) by using quadratic formula.

  $\begin{array}{l}\text{If}:a{x}^2+bx+c=0,\text{then}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ -16t^2+64t-60=0\\ a=-16;b=64;c=-60\\ t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ t=\frac{-64\pm \sqrt{{64}^2-4·-16·-60}}{2·-16}=\frac{-64\pm \sqrt{4096-3840}}{-32}=\frac{-64\pm \sqrt{256}}{-32}=\frac{-64\pm 16}{-32}\\ t=\frac{-64+16}{-32}\text{and}\frac{-64-16}{-32}\\ t=1.5\text{and}2.5\end{array}$

Thus, it takes 2.5 seconds for the rider to drop from 60 feet to zero feet.