Chapter 8.5, Problem 48AYU

To determine

To find:The equation that relates a rider’s height above the ground at time t.

Answer to Problem 48AYU

The equation of motion for the given condition is $d=97.5-82.5\cos \left(1.6t\pi \right)$ .

Explanation of Solution

Given:

The diameter of the Colossus is 165 feet, rotates at a rate of about 1.6 revolutions per minute and the bottom of the wheel is 15 feet above the ground.

The passenger begins the ride at the bottom of the wheel.

Calculation:

Based on the given data,

  $\begin{array}{c}\omega =1.6\\ a=\text{radius of the wheel}\\ =\frac{165}{2}\\ =82.5\end{array}$

By this information, the general equation of motion of the rider becomes $d=82.5\cos \left(1.6t\pi \right)$ .

Also, at time $t=0$ , the height of the rider above the ground is 15 feet.

So, in order to incorporate this condition, the equation of motion that describes the rider’s height above the ground becomes:

  $\begin{array}{c}d=15+\left[82.5\left(1-\cos \left(1.6t\pi \right)\right)\right]\\ =15+82.5-82.5\cos \left(1.6t\pi \right)\\ =97.5-82.5\cos \left(1.6t\pi \right)\end{array}$