Results 1 to 4 of 4

Math Help - pulley problem

  1. #1
    Junior Member winterwyrm's Avatar
    Joined
    Oct 2007
    Posts
    67

    pulley problem

    A worker sets up a pulley 12 meters high,
    to move a box with a rope of length 28 meters. If the
    worker moves to the left at 1
    2 meter per second, then
    at what rate does the box move along the ground
    when the worker is 5 meters from point A ?
    [IMG]file:///C:/Users/WINTER%7E1/AppData/Local/Temp/moz-screenshot.jpg[/IMG]
    Thanks in advance for any help. Btw, as a hint, it's a triangle problem, there's a diagram, but it won't copy/paste properly.

    s/n kk, got the diagram attached, thanks again =]
    Attached Files Attached Files
    Last edited by winterwyrm; October 27th 2007 at 08:57 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Without the diagram we cannot see the relationships of the given facts. Where is point A?
    Can you at least describe the figure?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by winterwyrm View Post
    A worker sets up a pulley 12 meters high,
    to move a box with a rope of length 28 meters. If the
    worker moves to the left at 1
    2 meter per second, then
    at what rate does the box move along the ground
    when the worker is 5 meters from point A ?
    [IMG]file:///C:/Users/WINTER%7E1/AppData/Local/Temp/moz-screenshot.jpg[/IMG]
    Thanks in advance for any help. Btw, as a hint, it's a triangle problem, there's a diagram, but it won't copy/paste properly.
    Use the manage attachments buttion below the message entry box (use
    the advanced editor), and upload the image, or provide a link to a copy
    uploaded to am image hosting service.

    RonL
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    So that is the figure. As I thought, point A is vertically below the pulley.

    Since the worker and the box are assumed to be points on the horizontal ground, we can solve the Problem if we assign distances from point A for the worker and the box.
    Let x = distance from worker to point A.
    And y = distance from box to point A.

    Two right triangles are formed.

    In the right triangle with the worker, the length of the rope is
    sqrt(x^2 +12^2)

    In the right triangle with the box, the rope is
    sqrt(y^2 +12^2)

    Then,
    sqrt(x^2 +144) +sqrt(y^2 +144) = 28 ------(i)

    The Problem needs to find rate of movement of the box along the ground, and the worker is given (1/2) m/sec rate, so we need to differentiate both sides of (i) with respect to time t to find dy/dt.

    [x /sqrt(x^2 +144)](dx/dt) +[y/sqrt(y^2 +144)](dy/dt) = 0 -----(ii)

    At the instant x = 5m, what is y?

    At that instant, the length of the rope with the worlker is
    sqrt(5^2 +144) = sqrt(169) = 13m

    So, in the right triangle with the box,
    the length of the rope is 28 -13 = 15m.
    hence,
    y = sqrt(15^2 -144) = sqrt(81) = 9m

    Substitute those int (ii),
    [x /sqrt(x^2 +144)](dx/dt) +[y/sqrt(y^2 +144)](dy/dt) = 0
    [5 /sqrt(5^2 +144)](1/2) +[9 /sqrt(9^2 +144)](dy/dt) = 0
    [5/13](1/2) +[9/15](dy/dt) = 0
    dy/dt = -[5/26]/[9/15]
    dy/dt = -0.3205 m/sec -----the negative sign only means that y is decreasing.

    Therefore, at that instant, the box is moving towards point A at the rate of 0.3205 m/sec. -----------------answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Another pulley problem/resolving
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: May 11th 2011, 08:31 AM
  2. Problem with pulley
    Posted in the Math Topics Forum
    Replies: 6
    Last Post: May 8th 2011, 12:22 PM
  3. [SOLVED] Need help with pulley problem
    Posted in the Geometry Forum
    Replies: 8
    Last Post: April 23rd 2010, 04:40 PM
  4. Belt & pulley problem
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 11th 2010, 11:10 PM
  5. Replies: 1
    Last Post: May 16th 2009, 05:09 AM

Search Tags


/mathhelpforum @mathhelpforum