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7 June, 00:54

To a cyclist riding west at 20 kg/hr, the rain appears to meet him at an angle of 45° with the vertical. When he rides at 12 km/hr, the rain meets him at an angle of 19°48' with the vertical. What is the actual direction of the rain?

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  1. 7 June, 02:57
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    Get the angle between the vertical and the line of sight of the cyclist parallel to the rain at 19°48’

    180 - 90 - 19°48’ = 70.2 °

    Prepare two equations to solve for the velocity of the rain

    DC2 sin 70.2 = (12 - x) tan 70.2

    DC1 tan 45 = (20 - x) tan 45

    Solving the equation results to

    x = 3.8

    and

    RD = 14.20

    The actual angle of the rain is,

    90 - tan-1 (14.20/3.8) = 15°
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