A revolving searchlight on an island 8 miles from the shore turns at a rate of 2 revolutions per minute in the clockwise direction. At what speed is the light beam traveling along the straight shoreline the instant it makes an angle of 45 degrees with the shoreline? (recall 1 revolution = 2pi radians). Answer in unite of miles/min.

Question

campbell_st · Answer

find the circumference of the circle formed by the light

radius = 8 miles... 

so 1 revolution of the circumference takes 30 sec

so when you get the circumference in terms of pi... double it to get the speed in miles per minute. 

45 degrees is 1/8 of a revolution. 

so find 1/8 of the speed. 

hope it helps.