Chapter 9.4, Problem 63SR

To determine

Find the time needed to fall from 250 feet to 40 feet.

Answer to Problem 63SR

It takes about 3.6 seconds to complete the ride.

Explanation of Solution

Given:

A popular amusement park ride whisks riders to the top of a 250 − foot tower and drops them. A function for the height of a rider is $h=-16t^2+250$ , where h is the height and t is the time in seconds. The ride stops the decent of the rider 40 feet above the ground. Write an equation that models the drop of the rider. Concept Used:

The ride stops the descent of the rider at 40 feet above ground, so $h=40\text{feet}$ .

Then, the equation $40=-16t^2+250$ models the drop of the rider.

Calculation:

The ride stops the descent of the rider at 40 feet above ground, so $h=40\text{feet}$ .

Then, the equation $40=-16t^2+250$ models the drop of the rider.

  $\begin{array}{l}h=-16t^2+250\\ 40=-16t^2+250\\ 40-250=-16t^2+250-250\\ -210=-16t^2\\ \frac{-210}{-16}=\frac{-16t^2}{-16}\\ t^2=13.125\\ \sqrt{t^2}=\sqrt{13.125}\\ t\approx \pm 3.6\end{array}$

Time cannot be negative. So, it takes about 3.6 seconds to complete the ride.

Thus, it takes about 3.6 seconds to complete the ride.