Q. 111 - Precalculus Enhanced with Graphing Utilities

Question

The Cable Cars of San Francisco At the Cable Car Museum you can see the four cable lines that are used to pull cable cars up and down the hills of San Francisco. Each cable travels at a speed of 9.55 miles per hour, caused by a rotating wheel whose diameter is 8.5 feet. How fast is the wheel rotating? Express your answer in revolutions per minute.

Step-by-Step Solution

Answer

The speed of the cable car is approximately $31.47$ rev/min.

Step 1. Given Information

Each cable travels at a speed of 9.55 miles per hour, caused by a rotating wheel whose

diameter is 8.5 feet.

Step 2. Forming the expression for rotation speed of the car

To find the speed of the rotation speed of the cable car, the formula for linear speed is needed, $v=rw,$ where $v=9.55$miles per hour and radius $r=\frac{d}{2}=\frac{8.5}{2}=4.25feet$

Step 3. Simplify for rotation speed

We have $$\begin{gathered} w=\frac{v}{r} \\ w=\frac{9.55mi/hr}{4.25ft} \end{gathered}$$

$$\begin{gathered} w=\frac{50424 rad}{160.2212253 min} \\ w=31.47 rev/min \end{gathered}$$