bahrom7893
Solution incoming..Need to figure out what I'm doing wrong.
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bahrom7893
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A driver needs to drive her car across a 180m long canyon. The side of the canyon opposite his starting point is 40m lower than the side that he's starting on. His initial speed is 50 m/s. At what smallest possible angle should a ramp be built so that he makes it across the canyon.
bahrom7893
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So this is what I did..
bahrom7893
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\[V_{iy}=V_{i}Sin\theta\]
\[V_{ix}=V_{i}Cos\theta\]
\[y=-40m\]
\[x=180m\]
\[V_i=50(m/s)\]
\[\theta-?\]
bahrom7893
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\[y = V_{iy}t+(1/2)at^2=>-40=V_{iy}t-4.9t^2\]
bahrom7893
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\[V_{iy}=V_iSin\theta=50Sin\theta\]
\[-40=50(Sin\theta)t-4.9t^2\]
\[x=V_{ix}t+(1/2)at^2=V_{ix}t=>180=50(Cos\theta)t=> t=18/(5Cos\theta)\]
bahrom7893
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After I plug in the value of t into:
\[-40=50(Sin\theta)t-4.9t^2\]
differentiate and solve for t, i get a crazy answer. Does anyone know why?
bahrom7893
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@TuringTest @anemonix
bahrom7893
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@AccessDenied @satellite73 @amistre64
bahrom7893
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Gotta run to a store, will be back in about half an hour, would appreciate it if anyone could take a look at this and tell me what's wrong with my solution.
bahrom7893
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yay Turing's here
TuringTest
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give me a minute to finish breakfast plz
bahrom7893
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Ok lol.. i just started eating breakfast too actually hahah
TuringTest
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first thing I gonna do when my hands are more free is draw it... I always draw it
rajathsbhat
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>.> i got 8.27 degrees actually.
bahrom7893
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|dw:1348331215780:dw|
bahrom7893
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What was the equation that you differentiated?
-40=180Tan(theta) - 63.5(Sec(theta))^2 ?
TuringTest
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I don't think differentiation is required
rajathsbhat
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just write sec^2(theta) as 1+tan^2(theta).
bahrom7893
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ohhhhhhh
bahrom7893
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never am i going to trust wolf ever again..
TuringTest
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good choice :)
bahrom7893
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-40 = 180Tan(theta) -63.5(Sec(theta))^2 and just solve for theta right?
rajathsbhat
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yup.
bahrom7893
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thanks a lot guys