Calculus

A gallon rises at the rate of 8 feet per second from a point on the ground 12 feet from an observer. To 2 decimal places in radians per second, find the rate of change of the angle of elevation when the ball on is 9 feet above the ground. Type your answer in the space bellow. If your answer is a number less than 1, place a leading "0" before the decimal point (ex:0.35)

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  1. Make your sketch. (What is rising, a gallon, a ball or a balloon ????)

    let the height of "whatever is rising" be y ft
    let the angle of elevation be Ø
    tanØ = y/12
    y = 12 tanØ
    dy/dt = 12sec^2 Ø dØ/dt

    in your sketch, let y = 9
    then h^2 = 12^2 + 9^2 = 225
    h = 15
    then cosØ = 12/15 = 4/5
    secØ = 5/4
    sec^2 Ø = 25/16

    now you got all your values to put into
    dy/dt = 12sec^2 Ø dØ/dt

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  2. Yes I'm sorry, i meant to type "balloon". I'm still a little confused, can you give me the exact number that is the answer so I can better understand please?

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  3. Giving you the "exact" number, will not help you understand it, the solution I gave you
    will help you understand it.

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  4. ok but I need to finish with the exercise with the answer but I don't understand. Can you finish with my question please?

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