Question

A rotating beacon is located 1 kilometer off a straight shoreline. If the beacon rotates at a rate of 3 revolutions per minute, how fast (in kilometers per hour) does the beam of light appear to be moving to a viewer who is 1/2 kilometer down the shoreline?

Answer 1

find the radius of the circle by finding the distance between the viewer and the beacon. 
then find the circumference by using 2πr2

this will be the distance the light covers over 1 revolution.
then using dimensional analysis:
3 rev/min (7.037 km/rev) (60 min/1 hr) = 1266.7 km/hr