calculus

A man in a rowboat at p, see fig 2c, 5km from the nearest point A on the straight shore. He wished to reach a point B, 6km from A along the shore, in a shortest time. Where should he land if he can row 2km/h and walks 4km/h?

P


5 km


A C B

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asked by dinesh
  1. Unfortunately we cannot see fig 2c unless you describe it or send a link.

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    posted by MathMate
  2. i cant attach the triangle...

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    posted by dinesh
  3. If this is a typical problem, then if he lands at a distance x from A, then the distance on water is

    √(x^2+5^2)

    and the distance on land is 6-x

    So, the time taken is

    t = √(x^2+25)/2 + (6-x)/4
    dt/dx = x / 2√(x^2+25) - 1/4
    = (2x-√(x^2+25)) / 4√(x^2+25)

    dt/dx=0 when x=5/√3
    at that point, the minimum t = (6+5√3)/4

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    posted by Steve
  4. Don't get it ?? Help!!

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    posted by Ana

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