1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Optimization -writing and solving the equations

  1. Dec 12, 2009 #1
    Im trying to write an equation for the question below. Could someone please point me in the right direction with writing it?
    1. The problem statement, all variables and given/known data

    An island is 4km from the nearest point p on the straight shoreline of a lake. if a person can row a boat at 3km/h and walk at 5km/h where should the boat be landed to arrive at a town 10km away is the least time?

    2. Relevant equations

    3. The attempt at a solution
    I think the equation is y=(1/3)*(4^2+x^2)^(1/2)+((10-x)/5)

    this doesn't look hard to differentiate but i cant seem to get the right answer-
    in fact i get imaginary numbers

    this is what i did

    y'= -1/5+1/2*1/3(16+x^2)^(1/2)*2x
    y'= -1/5+(2x/(6(16+x^2)^(1/2))
    3*(16+x^2)^(1/2)=5*x //square both sides
    x= +/- 6i //this is obviously wrong as a person does not travel imaginary distances
  2. jcsd
  3. Dec 12, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Poppynz! Welcome to PF! :smile:

    (have a square-root: √ and try using the X2 tag just above the Reply box :wink:)
    oops! :redface: … you forgot to square the 5, so you got 5 - 9 instead of 25 - 9 :rolleyes:

    Try again! :smile:
  4. Dec 12, 2009 #3
    haha such a silly mistake thanks :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook