Question

The blades on a wind turbine trace a circular path with radius 100 feet. Suppose the turbine spins at 20 revolutions per minute. What is the linear velocity, in miles per hour (1 mile equals 5,280 feet), of a point on the tip of a blade? Round the answer to the nearest tenth.

Answer 1

Radius = r = 100 feet
Angular velocity = w= 20 revolutions per minute = 20 x 2π radians per minute
Angular velocity = w = 40π radians per minute

Linear velocity = v = r w

So,

Linear velocity = v = 100 x 40π = 4000π feet per minute
v = 4000π x 60/5280 miles per hour
v = 142.8 miles per hour

Thus the Linear Velocity of the turbine will be 142.8 miles per hour

Answer 2

Answer:

The speed of the tip of the blade is 22.7 miles per hour.

Step-by-step explanation:

The blades on a wind turbine trace a circular path. The radius of the circular trace is $r=100$ ft.

The turbine spins with $N=20$ revolutions per minute.

Now, the linear velocity of the tip of the blade will be,

$v=rN\\v=100\times20\rm {ft/min}\\\mathit v=2000\rm ft/min$

Now, 1 mile is equal to 5280 feet and 1 hour is equal to 60 minutes.

So, the velocity of the tip of the blade in miles per hour will be,

$v=2000\times \dfrac{60}{5280}\\v=22.7\rm miles/hr$

Therefore, the speed of the tip of the blade is 22.7 miles per hour.

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