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Math Help - [SOLVED] Related rates problem for calculus

  1. #1
    Newbie ballet_dansur13's Avatar
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    Exclamation [SOLVED] Related rates problem for calculus

    A hot-air balloon is rising straight up from a level field and is tracked by a range finder 500 ft from lift-off point. the balloon rises at a rate of 15 feet per second.

    A) How fast is the direct distance between the range finder and the ballon changing at 5 seconds

    B) how fast is the angle of elevation changing when the ballon is 500 feet high


    he gave us a diagram of a right trianle with the hypotenus labeled d and the side labled h and the bottom equalling 500
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ballet_dansur13 View Post
    A hot-air balloon is rising straight up from a level field and is tracked by a range finder 500 ft from lift-off point. the balloon rises at a rate of 15 feet per second.

    A) How fast is the direct distance between the range finder and the ballon changing at 5 seconds

    B) how fast is the angle of elevation changing when the ballon is 500 feet high


    he gave us a diagram of a right trianle with the hypotenus labeled d and the side labled h and the bottom equalling 500
    also label the angle of elevation something. say  \theta

    Then we have the following relationship using trig ratios:

    \cos \theta = \frac {500}d

    that is,

    \cos \theta = 500d^{-1}

    now differentiate implicitly with respect to t (time) and continue (can you?)
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