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Math Help - Thinking and Inquiry Problem, Logarithmic Differentiation

  1. #1
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    Thinking and Inquiry Problem, Logarithmic Differentiation

    Hey guys, this is my first post and of course first question to ask of calculus

    Alright well I had this test and we had this very difficult question that I could not solve, it was in the hardest section.

    The question is as follows:
    A projectile thrown over level ground, at an angle x to the ground, has a range R given by R = (v^2 / g)(sin2x), where v is the initial speed, in meters per second, and g = 9.8m/s^2. Determine the angle of proection x for which the range is maximum.

    So I began to isolate for v^2 and then use log differentiation.

    R(g) = v^2(sin2x)
    v^2 = Rg / sin2x

    R = (v^2 / g)(sin2x)
    R = ((v^2)(sin2x) / g)
    ln R = ln v^2 + ln Sin2x - ln g
    dR / dx = [(1 / v^2) + (1 / sin2x) - (1 / g)] (v^2(sinx) / g)

    So im pretty sure that derrivative is right but as of this i am clueless on what to do. Any help is really appreciated, even a guideline so I could figure out the rest myself. Thanks.
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  2. #2
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    Quote Originally Posted by vexon View Post
    Hey guys, this is my first post and of course first question to ask of calculus

    Alright well I had this test and we had this very difficult question that I could not solve, it was in the hardest section.

    The question is as follows:
    A projectile thrown over level ground, at an angle x to the ground, has a range R given by R = (v^2 / g)(sin2x), where v is the initial speed, in meters per second, and g = 9.8m/s^2. Determine the angle of proection x for which the range is maximum.

    So I began to isolate for v^2 and then use log differentiation.

    R(g) = v^2(sin2x)
    v^2 = Rg / sin2x

    R = (v^2 / g)(sin2x)
    R = ((v^2)(sin2x) / g)
    ln R = ln v^2 + ln Sin2x - ln g
    dR / dx = [(1 / v^2) + (1 / sin2x) - (1 / g)] (v^2(sinx) / g)

    So im pretty sure that derrivative is right but as of this i am clueless on what to do. Any help is really appreciated, even a guideline so I could figure out the rest myself. Thanks.
    this does not require logarithmic differentiation, in fact, it doesn't even require calculus.

    see the linked thread ...

    http://www.mathhelpforum.com/math-he...sing-trig.html
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