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

Answer:

$\Delta t = 375\,s$

Step-by-step explanation:

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

$\omega = \frac{v}{R}$

$\omega = \frac{6.7\,\frac{ft}{s} }{4\,ft}$

$\omega = 1.675\,\frac{rad}{s}$

$\dot n = 0.267\,\frac{rev}{s}$

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

$\Delta t = \frac{n}{\dot n}$

$\Delta t = \frac{100\,rev}{0.267\,\frac{rev}{s} }$

$\Delta t = 374.532\,s$