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Math Help - A balloon rising?

  1. #1
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    A balloon rising?

    "A balloon is rising vertically above a level, straight road at a constant rate of 4 ft/sec. Just when the balloon is 56 feet above the ground, a bicycle moving at a constant rate of 17 ft/sec passes under it.

    a) How fast is the distance s(t) between the bicycle and the balloon increasing 3 seconds later?

    b) How fast is the angle between y(t) and s(t) changing at that time?"
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  2. #2
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    Quote Originally Posted by JessicaWade View Post
    "A balloon is rising vertically above a level, straight road at a constant rate of 4 ft/sec. Just when the balloon is 56 feet above the ground, a bicycle moving at a constant rate of 17 ft/sec passes under it.

    a) How fast is the distance s(t) between the bicycle and the balloon increasing 3 seconds later?

    b) How fast is the angle between y(t) and s(t) changing at that time?"
    (a) s^2 = (17t)^2 + (56+4t)^2

    find \frac{ds}{dt} at t = 3

    (b) \tan{\theta} = \frac{17t}{56+4t}

    find \frac{d\theta}{dt} at t = 3
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