Question

1. a wind machine used to generate electricity has blades that are 10 ft in length. the propeller is rotating at 4 revolutions per second. find the linear speed of the tips of the blades in ft/min.

Explanation:

Step1: Convert rotations per second to per minute

There are 60 seconds in a minute. Given 4 revolutions per second, the number of revolutions per minute is $4\times60 = 240$ revolutions per minute.

Step2: Calculate the circumference of the circle traced by the blade - tip

The formula for the circumference of a circle is $C = 2\pi r$, where the radius $r$ of the circle traced by the tip of the blade is the length of the blade. Here, $r = 10$ ft, so $C=2\pi(10)=20\pi$ ft.

Step3: Find the linear - speed

The linear speed $v$ is the product of the number of revolutions per minute and the circumference of the circle traced by the blade - tip. So $v=240\times20\pi$ ft/min.
$v = 4800\pi\approx4800\times 3.14 = 15072$ ft/min.

Answer:

$15072$ ft/min