Caculas

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(Airplane & Radar) An airplane is flying (horizontally) at the height of 6 km on a flight path that will take it
directly over a radar tracking station (on ground). If the distance D between the plane and the radar is
decreasing at a rate of 300 km/hr, find the speed of the plane when D remains 10 km.

  • Caculas -

    x^2 + h^2 = D^2
    solve for x when D = 10 and h = 6
    x = 8 (3,4,5 triangle)

    2 x dx/dt + 2 h dh/dt = 2 D dD/dt
    but dh/dt = 0
    so
    2 (8)v + 0 = 2 (10) 300

    v = 3000/8

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