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 times 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 1.23 10-7 s in round-trip times for two pulses that are emitted 0.440 s apart. Assuming that the speeding vehicle is approaching the police car essentially head-on, determine the speed of the vehicle.

Explanation / Answer

Since the car travels 1.23*10-7 seconds of light speed ,

Distance travelled d = (3*108 m/s)(1.23*10-7s)

                            d = 36.9 m

Time t = 0.440 s

As we are considering the 0.440 s time difference for two pulses emitted is for the distance travelled for

the two pulses round trip, we have to devide the distance by 2.

            therefore, d = 36.9 m / 2

                            d = 18.45 m

Therefore, velocity v = d / t

                             v = 18.45 m / 0.440 s

                             v = 41.93 m/s

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