Chapter 12.3, Problem 36PPS

To determine

To find: How high above the ground is the car when it has stopped.

Answer to Problem 36PPS

The height above the ground to the car is $145.8$ feet.

Explanation of Solution

Given information:

Radius of Ferris wheel $=r=68$ feet

Ferris wheel is $15$ feet off the ground

  $\theta ={202.5}^0$

Given

Radius of Ferris wheel $=r=68$ feet

Ferris wheel is $15$ feet off the ground

  $\theta ={202.5}^0$

Since, the angle measured from the negative y-axis,

The terminal angle $=\theta ={202.5}^0-{90}^0={112.5}^0$

As ${112.5}^0$ is present in Quadrant-II

Reference angle is

  $\begin{array}{l}{\theta }^{\text{'}}={180}^0-\theta \\ \Rightarrow {\theta }^{\text{'}}={180}^0-{112.5}^0\\ \Rightarrow {\theta }^{\text{'}}={67.5}^0\end{array}$

We know

  $\sin \left(\theta \right)=\frac{y}{r}$

On substituting values

We get

  $\begin{array}{l}\sin \left(\theta \right)=\frac{y}{r}\\ \Rightarrow \sin \left({67.5}^0\right)=\frac{y}{68}\\ \Rightarrow y=68\sin \left({67.5}^0\right)\\ \Rightarrow y=68\left(0.9238\right)\\ \Rightarrow y=62.8\end{array}$

Therefore,

The height above the ground to the car is $=62.8+68+15=145.8$ feet.