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 is a stationary police car observes a difference of 1.22 × 10-7 s in round-trip travel times for two pulses that are emitted 0.490 s apart. Assuming that the speeding vehicle is approaching the police car essentially head-on, determine the speed of the vehicle.

Explanation / Answer

Solution:-

From the question, the car travels 1.22 × 10-7 seconds of light speed,
Distance travelled d = (3*10^8 m/s)(1.22*10-7s)
                            d = 36.6 m
Time t = 0.490s
here we are considering the 0.490s time difference for two pulses emitted is for the distance travelled for
the two pulses round trip, therefore we have to divide the distance by 2.
    
            therefore, d = 36.6 m / 2
               
                            d = 18.3 m
Hence, velocity v = d / t
                             v = 18.3 m / 0.490 s
                            v =   37.35 m/s

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