Question

A paddle wheel on a boat is 8 feet in diameter. The fins along the outer edge travel at a speed of 6.7 feet per second. How long does it take the

paddle wheel to complete 100 full revolutions? Round to the nearest second

Answer 1

`\Delta t = 375\,s`

Explanation:

The angular speed of the paddle wheel is determined by the following expression:

`\omega = (v)/(R)`

`\omega = (6.7\,(ft)/(s) )/(4\,ft)`

`\omega = 1.675\,(rad)/(s)`

`\dot n = 0.267\,(rev)/(s)`

The time required for the paddle wheel to complete 100 revolutions is:

`\Delta t = (n)/(\dot n)`

`\Delta t = (100\,rev)/(0.267\,(rev)/(s) )`

`\Delta t = 374.532\,s`