A stationary speed gun emits a microwave beam at 2.10*10^10Hz. It reflects off a car and returns 1030 Hz higher. What is the speed of the car?

Answer: V = 15 m/s

Explanation:

As stationary speed gun emits a microwave beam at 2.10*10^10Hz. It reflects off a car and returns 1030 Hz higher. The observed frequency the car will be experiencing will be addition of the two frequency. That is,

F = 2.1 * 10^10 + 1030 = 2.100000103*10^10Hz

Using doppler effect formula

F = C / (C - V) * f

Where

F = observed frequency

f = source frequency

C = speed of light = 3*10^8

V = speed of the car

Substitute all the parameters into the formula

2.100000103*10^10 = 3*10^8 / (3*10^8 - V) * 2.1*10^10

2.100000103*10^10/2.1*10^10 = 3*108 / (3*10^8 - V)

1.000000049 = 3*10^8 / (3*10^8 - V)

Cross multiply

300000014.7 - 1.000000049V = 3*10^8

Collect the like terms

1.000000049V = 14.71429

Make V the subject of formula

V = 14.71429/1.000000049

V = 14.7 m/s

The speed of the car is 15 m/s approximately.