Question

A revolving searchlight on an island 6 miles from shore turns at the rate of 2 revolutions per minute in the clockwise direction. At what speed is the light beam travelling along the straight shoreline the instant it makes an angle of 45◦ with the shoreline? (recall: one revolution = 2π radians.)

Answer 1

Answer:

 Revolving velocity = 2 km/s

Explanation:

Velocity of circular motion = Radius x Angular velocity.

Angular velocity, ω = 2πf, where f is the frequency of circular motion.

Here frequency, f = 2 revolutions per minute

                     f = $\frac{2}{60} =0.033$revolutions per second.  

Angular velocity, ω = 2πf = 0.209 radians/second.

Radius = 6 miles = 6 x 1.6 x 10³ = 9.6 x 10³ m.

Linear velocity =  9.6 x 10³ x 0.209 = 2006.4 m/s= 2 km/s

Revolving velocity = 2 km/s