Answer:
The speed of the car is 14.7m/second or 15 m/second approximately.
Explanation:
A microwave beam at [tex]2.10\times10^1^0Hz[/tex] is generated by a stationary speed gun. It bounces off a car and returns at a higher frequency of 1030 Hz. The car's observed frequency would be the product of adding the two frequencies. That is to say,
F =[tex]2.1\times10^1^0+1030[/tex] =[tex]2.100000103\times10^1^0Hz[/tex]
Using doppler effect formula
[tex]F=\frac{C}{C-V}\times f[/tex]
Where
F = observed frequency
f = source frequency
C = speed of light = [tex]3\times10^8[/tex]
V = speed of the car
Putting the values in the formula -
[tex]2.100000103\times10^1^0=\frac{3\times10^8}{3\times10^8-V}\times2.1\times 10^1^0[/tex]
[tex]\frac{2.100000103\times10^1^0}{2.1\times10^1^0}[/tex] [tex]=\frac{3\times10^8}{3\times10^8-V}[/tex]
[tex]1.000000049=\frac{3\times10^8}{3\times10^8-V}[/tex]
by cross multiplication ,
300000014.7 - 1.000000049V = [tex]3\times10^8[/tex]
Collect the like terms
1.000000049V = 14.71429
Make V the subject of formula
V = [tex]\frac{14.71429}{1.000000049}[/tex]
V = 14.7 m/s
Therefore , the speed of the car is 15m/second approximately.
