Results 1 to 3 of 3

Math Help - [SOLVED] boat travels accross a river...

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    82

    [SOLVED] boat travels accross a river...

    A guy traveling 5m/s accross a 40m wide river (banks are parallel). The water speed is fastest in the middle. The speed for the water is given as: (3/400)(x)(40-x) where x is the meters from shore. (for ease of communication assue the river goes North and the guy is traveling West to East).

    1) How far down does he travel?
    2) At what angle South (upstream) does he need to travel to end up directly accross the river from where he started.

    My work: It takes him 8 seconds to cross the river because his speed is constant. From here I am not sure where to begin. I am pretty sure that there is an integral involved to "add up" all the downward drif but i cannot get it to work out.
    As for the second part this should (i think) be easy because given that it is 40 meter accross and "Z" feet downstream is what he ended up. I can just use tangent to figure out that angle and say to go upstream.

    Thanks....and sorry for spelling errors it clears my text as i found out
    Last edited by snaes; September 21st 2009 at 05:29 PM. Reason: grammer & spelling error
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by snaes View Post
    A guy traveling 5m/s accross a 40m wide river (banks are parallel). The water speed is fastest in the middle. The speed for the water is given as: (3/400)(x)(40-x) where x is the meters from shore. (for ease of communication assue the river goes North and the guy is traveling West to East).

    1) How far down does he travel?
    2) At what angle South (upstream) does he need to travel to end up directly accross the river from where he started.

    My work: It takes him 8 seconds to cross the river because his speed is constant. From here I am not sure where to begin. I am pretty sure that there is an integral involved to "add up" all the downward drif but i cannot get it to work out.
    As for the second part this should (i think) be easy because given that it is 40 meter accross and "Z" feet downstream is what he ended up. I can just use tangent to figure out that angle and say to go upstream.
    v_x= 5 m/s , so x = 5t

    sub 5t for x in the water speed expression ...

    v_y = \frac{3(5t)}{400}(40-5t)

    to get the distance downstream ...

    \int_0^8 v_y \, dt


    for the second part, I don't think the angle steered upstream is a constant ... I'll have to think on that.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    82
    Thanks that makes sense now. I actually treid that in my calculator only typed in wrong . Thanks, the explanation helped my understanding more though.

    For number 2) if this helps you think: (I do the homework for comprehension not for a grade so take your time...)

    Answer in back:It's approxonately 23.6 deg upstream and it shows a graph that has has xmin0 to xmax40 then line goes down that back up (like a -sin(x) but with period of 40) symetrically along the x axis. It has a zero at 20 and probably (just guessing by looking at graph) has a max of about 2. So the equation has to be somewhat close to -2sin[.05*pi*x].

    You are correct that the angle would not be constant: Because the inverse tangent of (16/40)=21.8deg which obvioulsy is close but wrong.
    Last edited by snaes; September 21st 2009 at 06:01 PM. Reason: oops
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: February 2nd 2011, 08:03 AM
  2. Replies: 5
    Last Post: October 15th 2010, 04:41 AM
  3. Trajectory of a boat across a river- differential equations
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: April 13th 2008, 08:43 PM
  4. A car travels...
    Posted in the Algebra Forum
    Replies: 4
    Last Post: July 18th 2006, 04:18 AM
  5. If car A travels faster than car B . . .
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 12th 2005, 11:08 PM

Search Tags


/mathhelpforum @mathhelpforum