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Math Help - derivatives velocity

  1. #1
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    derivatives velocity

    I need to check my answers on part a, and see what's wrong on b. Also, what units do i use?

    An abnormal projectile is shot in the air, so that after t seconds, its height in feet is
    a) find the velocity at times 0 and 5
    b) When is it highest? When does it land?

    my answers:
    I have the derivative as -7tan(\frac{x}{2}+1.67)
    a) @t=0, 70.33 (units?)
    @t=5, -11.6 (units?)

    b) I wasn't totally sure how to do it, so I set the derivative equal to 0. I thought that that should give me the max height, but I came out with -3.34, which is obviously wrong. Did i make a math error or should I not have set it equal to 0? please help!
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  2. #2
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    Hi

    Is the angle unit specified (degree, radian) ?
    You have assumed it is radian. In this case are you sure about +1.67 ? I mean if it was +1.57, we could say that it is \frac{\pi}{2}

    In any case due to ln domain )0,+\infty( we must have -\cos\left(\frac{x}{2}+1.67\right) > 0 \Rightarrow -\frac{\pi}{2} < \frac{x}{2}+1.67 < \frac{3\pi}{2}

    Setting the derivative to 0 is OK to find the maximum height.
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  3. #3
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    You are correct that s'(t)=-7\,\tan\left(\frac{x}{2}+1.67\right).

    To find the maximum height, we find the point at which s'(t)=0:

    \begin{aligned}<br />
-7\,\tan\left(\frac{x}{2}+1.67\right)&=0\\<br />
\tan\left(\frac{x}{2}+1.67\right)&=0.<br />
\end{aligned}<br />

    Hint: \tan x measures the slope of an angle. When does \tan x = 0? For what value of x is \ln \left(-\cos\left(\frac{x}{2}+1.67\right)\right) defined?
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  4. #4
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    also

    thanks to both of you, i got 2.94, which makes sense. and jsyk, assumed angle measure is radians

    So how do I find out when it lands? that I have no idea how to do...
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  5. #5
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    To find where it lands, we solve

    14\ln\left(-\cos\left(\frac{x}{2}+1.67\right)\right)+34=0.

    Before we take \arccos, we must remember that there will be two solutions to consider.
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  6. #6
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    wow...

    Quote Originally Posted by Scott H View Post
    To find where it lands, we solve

    14\ln\left(-\cos\left(\frac{x}{2}+1.67\right)\right)+34=0.

    Before we take \arccos, we must remember that there will be two solutions to consider.
    O yeah...I was thinking that i had to do something with the derivative to find where it lands...ok...now i feel smart. thanks!
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  7. #7
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    for part a, (assuming this is a calculator active question), i would pop s(t) into the Y1 of a TI calculator and use nDerive(Y1,x,0) and nDerive(Y1,x,5). I get the same answers you do: 70.33 and -11.61. since velocity is the rate of distance over time, the units are feet per second.

    Hope this helps
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