## Answers

In terms of tangential velocity, the tip is traveling 110.432 miles per hour faster than the root of the windmill blade.

#### Explanation:

The first step is to determine the angular velocity of the windmill's rotor.

Angular Velocity is given in radians per second. Since the windmill makes a full rotation in 4.5 seconds, and one rotation is

To find the *Tangential Velocity*, or the linear velocity at a given radius, we need simply to multiply the Angular Velocity by the desired radius:

To determine the difference in Tangential Velocities, we would simply subtract one from the other. Since both points are traveling at the same Angular velocity, we can simplify the equation somewhat:

Now, because we've written the equation this way, knowing the discrete radii of the base and tip is irrelevant. We only need to know the distance between the radii.

Based on the problem statement, we know the length of the blade, which is the distance we need: 116 feet.

Finally, now that we have the delta-velocity in feet per second, we need to convert to miles per hour: