Anonymous
Anonymous asked in Science & MathematicsMathematics · 10 years ago

Calculus question!!! see below...?

A dune buggy is on a straight desert road, 40 km north of Dustin City. The

vehicle can travel at 45 km/h off the road and 75 km/h on the road. The

driver wants to get to Gulch City, 50 km east of Dustin by another straight

road, in the shortest possible time. Determine the route he should take.

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  • M3
    Lv 7
    10 years ago
    Favorite Answer

    .. C

    .. |\ angle ACP = z.

    .. |-\

    w|--\

    ...|----\

    .. |-----\------

    ..A. x P ...B gulch city

    ...<---- y --->

    let dist. to dustin city = w (40 km)

    speed ratio regular road: desert road = k (5/3)

    dist. over desert = w•sec z,

    dist. over regular road = y - w•tan z

    time taken ∞ k•sec z +(y - tan z)

    dT/dz = k•secz•tan z - sec^2 z

    = (ksin z - 1) / cos^2 z

    for minima, sin z = 1/k

    which yields x = w /√(k^2 - 1)

    plugging in,

    x = 40/√((5/3)^2 - 1)

    ans: x = 30 km

    ------

    note that the optimal value of angle z is solely dependent on k !

  • 5 years ago

    Its (eleven+five)/(eleven+15) =sixteen/26 = sixty one.538% roughly. (Note: I'm assuming that it entails those who're freshman "and" feminine. So, if thats now not the case, my reply is flawed then. Sorry.)

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