a wind mill is used to generate electricity. the wind mill has propeller blades that are 12 feet in length. if the propeller is rotating at 3 revolutions per second, what is the linear speed in feet per seconds of the tips of the blades?

r=12

C = 2πr

3 rev/min * 24π ft/rev * 1min/60s = 72π/60 = 6π/5 ft/s

Well, it sounds like the windmill is really getting into the spin of things! So let's calculate the linear speed of those blade tips.

To do that, we first need to find out the distance a propeller blade travels in one revolution. Since the blades are 12 feet long, the circumference of their circular path would be 2π * 12 feet.

Now, if the propeller is rotating at 3 revolutions per second, we can multiply the circumference by the number of revolutions per second: 2π * 12 feet * 3 revolutions. This will give us the total distance traveled by the tip of the propeller in one second.

So, the linear speed of the propeller's tips would be 2π * 12 feet * 3 revolutions per second, which simplifies to about 226.19467105691 feet per second.

That's quite the whirlwind!

To find the linear speed in feet per second of the tips of the blades, we need to calculate the circumference of the circular path that the tips of the blades travel in one revolution, and then multiply it by the number of revolutions per second.

1. First, let's find the circumference of the circular path (C) that the tips of the blades travel in one revolution. The circumference of a circle is given by the formula:
C = 2πr, where r is the radius of the circle.

2. The radius of the circular path is equal to the length of the propeller blades, which is 12 feet.

r = 12 feet

3. Plugging the value of r into the circumference formula, we have:
C = 2π(12) = 24π feet

4. Now, we need to find the linear speed in feet per second. We can do this by multiplying the circumference by the number of revolutions per second.

Linear speed = C * number of revolutions per second
Linear speed = 24π * 3

5. Calculate the linear speed:
Linear speed ≈ 24π * 3 ≈ 72π feet per second

Therefore, the linear speed in feet per second of the tips of the blades is approximately 72π feet per second.

To find the linear speed of the tips of the windmill blades, we need to determine the distance covered by the tip of the blade in one revolution and then multiply it by the number of revolutions per second.

The length of the propeller blades is given as 12 feet, so the distance covered by the tip of the blade in one revolution is the circumference of a circle with a radius of 12 feet.

The circumference of a circle is given by the formula:

Circumference = 2 * π * radius

Substituting the value, we have:

Circumference = 2 * π * 12 feet

Next, we need to determine the distance covered by the tip of the blade in one second. Given that the propeller rotates at 3 revolutions per second, we can multiply the circumference by the number of revolutions per second:

Distance covered in one second = Circumference * 3 revolutions

Now, let's calculate it:

Circumference = 2 * π * 12 = 24π feet

Distance covered in one second = 24π feet * 3 revolutions

To get the linear speed in feet per second, we multiply the distance by the number of revolutions:

Linear speed = 24π feet/rev * 3 rev/second

Finally, we calculate the result:

Linear speed = 72π feet/second

So, the linear speed of the tips of the windmill blades is 72π feet per second.