Calculus Question..?

A boat on the ocean is 4 mi from the nearest point on a straight​ shoreline; that point is 14 mi from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. 

Minimize the time traveled, where would she land on shore?

Update:

 walks at 3​ mi/hr and rows at 2​ mi/hr

2 Answers

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  • david
    Lv 7
    3 weeks ago

    d = dist. rowed

    x = dist down the beach where she comes ashore

      ...x^2 + 4^2  = d^2

    distt walked  = 14 - x

    time rowed = d/r = d / 2

    time walked  =  (14-x)/3

      T = d/2 + (14-x)/3

      T = sqrt(x^2 + 16)/2 +  (14-x)/3

      T'  =  (1/2)(x^2 + 16)^(-1/2) *2x  +  -1/3

      T'  =  -x/sqrt(x^2 + 16) - 1/3  =  0 

          x/sqrt(x^2 + 16)  =  -1/3

            sqrt(x^2 + 16)   =  -3x

       x^2 + 16  =  9x^2

           8x^2 = 16

              x =  sqrt 2  .....  (neg will not be a min)

       

      from the point closest to the boat, she should come ashore  sqrt 2 miles down the beach from there.

  • 3 weeks ago

    This is an incomplete question. To solve it, the speed of rowing boat and that of walking along the shore should be given.

    • Emma3 weeks agoReport

      walks at 3​ mi/hr and rows at 2​ mi/hr

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