Calc Question Please Help

Question

Suppose that two​ 3-blade windmills rotate 6060 times per minute. What is the difference in linear velocity in miles per hour of the tips of the windmill blade if the larger windmill has 6060​-foot blades and the smaller windmill has 4040​-foot blades?

Answer 1

They rotate once per second, as 60 rotations per minute = 60 rotations per 60 seconds = 1 rotation per second

One entire circumference is traveled in 1 second.

For the 60 foot blades, the circumference is 2*pi*radius = pi*120 feet.

For the 40 foot blades, the circumference is 2*pi*radius = pi*80 feet

linear velocity * time = distance

so V = distance/time

1 hour = 60 minutes = 60 min * 60 sec/min = 3600 sec

So the linear difference in velocity is 3600 ft* ( pi *120) / hr - 3600* (pi * 80) / hr

= 3600 ft * pi * (120 - 80) / hr

= 3600 ft * pi * 40 / hr

1 mile = 5280 ft

3600/ 5280 * pi * 40 which is approximately equal to 85 and 5/7 mph, using pi=22/7

Answer 2

Not really a calculus question.

The ratio of radii is 3/2. Therefore the ratio of circumferences is 3/2.

The linear velocities would be in the ratio of 3/2.