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 1.27 × 10−7 s in round-trip travel times for two pulses that are emitted 0.450 s apart. Assuming that the speeding vehicle is approaching the police car essentially head-on, determine the speed of the vehicle.

Answer 1

Answer:

v = 42.33 m/s

Explanation:

The time difference between two pulses that are emitted by Police is observed in the interval

$\Delta t = 1.27 \times 10^{-7} s$

now the speed of the electromagnetic wave is given as

$c = 3 \times 10^8 m/s$

now the distance traveled by them

$d = c \times t$

$d = (3 \times 10^8)(1.27 \times 10^{-7})$

$d = 38.1 m$

so distance of speeding vehicle covered for round trip of wave is 38.1 m

now for one trip it is given as d = 19.05 m

now the speed of the vehicle is given as

$v = \frac{d}{t}$

$v = \frac{19.05}{0.450}$

$v = 42.33 m/s$