Results 1 to 7 of 7

Math Help - Applying derivatives

  1. #1
    Member
    Joined
    Feb 2008
    Posts
    97

    Applying derivatives

    Suppose you are swimming in a lake and find yourself 200m from shore. You would like to get back to the spot where you left your towerl, which is at least 200m down the beach, as quickly as possible. You can walk along the beach at 100m/min, but you can swim at only 50m/min. To what point of the beach should you swim to minimize your total travelling time?

    Is this function correct?

    T=(200-x)/100 + (sqrt(200^2+x^2))/50
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Apr 2008
    Posts
    65
    i am getting

    t(x) = x/100 + (((200-x)^2 + 200^2)^1/2) /50)

    as we can see if the guy swims all the way he will be going 80 000^1/2 at 50 m/min and will take him

    5.66 hours appx

    try x = 0 in both equations...

    here i am using the starting point at the bottom left of the diagram and the x value is the horizontal distance from the towel to the point that the swimmer reaches shore

    let me know what you think
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2008
    Posts
    65
    one second you might be right... let me try x = 200 for yours
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Apr 2008
    Posts
    65
    yeah okay i see what you did, we just had the diagram drawn differently
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Apr 2008
    Posts
    65
    im getting that he should swim to the point approximately 84.55 metres away from the towel

    i cant find the root of the derivative but i approximated a value very near to it

    what did you get?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Feb 2008
    Posts
    97
    I tried to find the derivative, got this:

    -1/100 + 1/(25(sqrt[200^2+x^2]))

    I seem to get a negative value for x^2 which doesn't make sense.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Apr 2008
    Posts
    65
    differentiating yours i get -1/100 + ( x / (50(200^2 + x^2)^1/2)

    try x = 84.55 in it and you will get -0.0022

    and try 200-84.55 which would be 84.55 away from the towel and you get -0.000013


    i think there might be two optimal positions for him to land on the shore
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Applying Mean Value Theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 16th 2011, 02:10 AM
  2. Applying the Law of Cosines
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: December 4th 2010, 03:39 PM
  3. Replies: 5
    Last Post: October 8th 2009, 04:35 AM
  4. Applying derivatives
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 29th 2008, 07:53 PM
  5. Factorising and applying!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 30th 2008, 02:24 AM

Search Tags


/mathhelpforum @mathhelpforum