Geometry question

Question

A paddle wheel on a boat is 8 feet in diameter. The fins along the outer edge travel at a speed of 6.7 feet per second. How long does it take the paddle wheel to complete 100 full revolutions? Round to the nearest second.

Answer 1

Distance equals velocity times time (d=vt).  Thus, v=d/t.

 

Velocity=speed = 6.7 ft/s.

 

Distance for one revolution = 2*pi*r (for a circle) = 2*pi*(4 ft) = 8*pi (radius equals 1/2 diameter).

 

6.7 equals (8*pi)/T.

 

Therefore, T=(8*pi)/6.7 (algebra).

 

Thus, time for one revolution equals T=3.751.

 

So the time for 100 full revolutions = 100*3.751 = 375.1 seconds