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5 November, 15:33

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?

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  1. 5 November, 18:51
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    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.
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