Arevolving 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.)

 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 = 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

when a device is used in a circuit in which the voltage is 81 v, the current flowing through the device is 3 a. what is the resistance of the device?

a. 27 ω

b. 40.5 a

c. 243 ω

d. 243 a

the correct answer is a. 27