Chapter 11.3, Problem 37PPS

(a)

To determine

To Find: The rational expression for the speed of a car rotating in time $t$

Answer to Problem 37PPS

  $speed=\frac{785.5}{t}$

Explanation of Solution

Given: To find the speed travelled by a car located on the wheel, you can find the circumference of a circle and divide by the time it takes for one rotation.

  

Given: distance = $250ft$

Radius= $\frac{250}{2}=125ft$

Then

Circumference of the circle = $2\pi r$

  $\begin{array}{l}=2\pi (125)\\ =2\times 3.14\times 125\\ =785.5\end{array}$

Then

  $\begin{array}{l}speed=\frac{circumference}{time}\\ time=t\\ speed=\frac{785.5}{t}\end{array}$

Hence, $speed=\frac{785.5}{t}$

(b)

To determine

To Find: The speed of the car on the circumference in feet per minute.

Answer to Problem 37PPS

  $157.1$ feet per minute

Explanation of Solution

Given: Suppose the first Ferris wheel rotated once in every $5$ minutes.

  

Given: $t=5\min$

Then

  $\begin{array}{l}speed=\frac{785.5}{t}\\ speed=\frac{785.5}{5}=157.1\end{array}$

Hence, the speed is $157.1$ feet per minute