Question

Plzzz help!! A stationary speed gun emits a

microwave beam at 2.10x1010 Hz. It
reflects off a car and returns 1030 Hz
higher. What is the speed of the car?
(Unit = m/s)

Answer 1

The speed of the car is 14.7m/second or 15 m/second approximately.

Step-by-step explanation:

A microwave beam at
`2.10*10^1^0Hz` 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 =
`2.1*10^1^0+1030` =
`2.100000103*10^1^0Hz`

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

Putting the values in the formula -

`2.100000103*10^1^0=(3*10^8)/(3*10^8-V)*2.1* 10^1^0`

`(2.100000103*10^1^0)/(2.1*10^1^0)`
`=(3*10^8)/(3*10^8-V)`

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

by cross multiplication ,

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

Therefore , the speed of the car is 15m/second approximately.