Chapter 14.2, Problem 42PPSE

Solution

To calculate : The time when the car first will be $30\text{ ft}$ off the ground.

The required time is $69\text{ sec}$ .

Given information :

The function $h=25\sin \left(\frac{\pi }{20}\left(t-10\right)\right)+34$ , models the height $h$ of aFerris wheelcar in feet, $t$ seconds after starting.

Calculation :

Given expression is $h=25\sin \left(\frac{\pi }{20}\left(t-10\right)\right)+34$ where $h$ is the height and $t$ is the time.

Substitute $h=30\text{ ft}$ in the given expression.

  $\begin{array}{l}30=25\sin \left(\frac{\pi }{20}\left(t-10\right)\right)+34\\ -4=25\sin \left(\frac{\pi }{20}\left(t-10\right)\right)\\ \frac{-4}{25}=\sin \left(\frac{\pi }{20}\left(t-10\right)\right)\\ \left(\frac{-4}{25}\right){\sin }^{-1}=\frac{\pi }{20}\left(t-10\right)\\ \left(\frac{-4}{25}\right){\sin }^{-1}\frac{20}{\pi }=t-10\\ t=\frac{20}{\pi }{\sin }^{-1}\left(\frac{-4}{25}\right)+10\end{array}$

Use the calculator to find the value of $t$ .

Since time cannot be negative, so negative value of $t$ is neglected.

Therefore, the required time is $69\text{ sec}$ .