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 1.32 x 10-7 s in round-trip travel times for two pulses that are emitted 0.400 s apart. Assuming that the speeding vehicle is approaching the police car essentially head-on, determine the speed of the vehicle.

________ m/s

Explanation / Answer

light travels at about 1 foot per nanosecond, so the time needed to travel 1000 feet, which is almost 300 m, is 1 microsecond.

the time interval between the arrival of the two pulses at the car can be approximated to be the same as the time interval between the emission of the two pulses

2d = ct1/2 = ct1/2

d = 3*10^8*1.32*10^-7/2 = 19.8 m

the speed of the car v = d/t2 = 19.8/0.4 = 49.5 m/s

v = 178.2 km/h

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