A lidar (laser radar) gun is an alternative to the standard radar gun that uses

Question

A lidar (laser radar) gun is an alternative to the standard radar gun that uses the Doppler effect to catch speeders. A lidar gun uses an infrared laser and emits a precisely timed series of pulses of infrared electromagnetic waves. The time for each pulse to travel to the speeding vehicle and return to the gun is measured. In one situation a lidar gun in a stationary police car observes a difference of 1.13 10^-7 s in round-trip travel times for two pulses that are emitted 0.460 s apart. Assuming that the speeding vehicle is approaching the police car essentially head-on, determine the speed of the vehicle.

Explanation / Answer

difference in time = 1.13 x 10-7 sec

difference in position is given as ::

(1.13 x 10-7 ) (3 x 108 ) / 2

where speed of light, c = 3 x 108 m/sec

(1.13 x 10-7 ) (3 x 108 ) / 2 = 16.95 m

speed = difference in position / time    {equation 1}

where, difference in position = 16.95 m

time = 0.460 sec

inserting value in equation 2,

speed, v =16.95 / 0.460 = 36.847 m/s

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