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9 April, 16:02

A plane flying with a constant speed of 29 km/min passes over a ground radar station at an altitude of 6 km and climbs at an angle of 25 degrees. At what rate is the distance from the plane to the radar station increasing 5 minutes later?

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  1. 9 April, 17:35
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    Step-by-step explanation:

    According to the diagram,

    A = 90° + 25° = 115°

    dc/dt = 29 km/min

    distance after 5 min

    c = 29 x 5 = 145 km

    Use cosine rule

    a² = b² + c² - 2bc Cos A

    a² = 6² + c² - 12cCos 115

    a² = 36 + c² - 5 c ... (1)

    When c = 145 km

    a² = 36 + 145 x 145 - 5 x 145

    a² = 21061 - 725

    a = 142.6 km

    Differentiate equation (1) with respect to a.

    2a da/dt = 2c dc/dt + dc/dt

    2 x 142.6 x da/dt = 2 x 145 x 29 + 29

    285.2 da/dt = 8439

    da/dt = 29.6 km/min
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