Results 1 to 3 of 3

Math Help - Inclined Plane Problem

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    40

    Cool Inclined Plane Problem

    Trying to figure this out. I know it relates to the fact that an inscribed angle subtended by a diameter is a right angle, but I can't put the answer into appropriate mathematical language:

    An objects slides down an inclined plane OP' starting from rest at O, which is the top of a circle of diameter OP, where P and P' lie in a horizontal line. Show that the point Q reached in the time, t, required to fall straight down from O to P lies on a circle with OP as diameter.

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,212
    Thanks
    419
    Awards
    1
    Quote Originally Posted by Ultros88 View Post
    Trying to figure this out. I know it relates to the fact that an inscribed angle subtended by a diameter is a right angle, but I can't put the answer into appropriate mathematical language:

    An objects slides down an inclined plane OP' starting from rest at O, which is the top of a circle of diameter OP, where P and P' lie in a horizontal line. Show that the point Q reached in the time, t, required to fall straight down from O to P lies on a circle with OP as diameter.

    Thanks.
    If I've got you right, this is the diagram.

    One question. The point Q lies on a circle of diameter OP. Where is the center of this circle supposed to be?

    -Dan
    Attached Thumbnails Attached Thumbnails Inclined Plane Problem-diagram.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2008
    Posts
    40

    Location of Center

    In the problem, it is not clear where the center is, only that OP passes through it. Hope that will help. This is my solution(?), please point out any problems or a simpler way withou using so much geometry if there is such an answer. Thanks.:

    The time, t, it takes to fall from O to P is t = sqrt(d(OP))/4.
    The distance along the inclined plane that the mass slides is given by the equation d(OQ) = 16(t^2)*Sin(A).
    In time t, d(OQ) = d(OP)*Sin(A).

    Drawing Q'P, where Q' is the intersection of OP' with the circle, we have a right triangle OPQ' because an inscribed angle subtended by a diameter is a right angle. Because angle OP'P and angle OPQ' are complementary to the same angle they are equal, that is OPQ' = A. Therefore d(OQ') = d(OP)*Sin(A) = d(OQ). Since OQ and OQ' are at the same angle from OP and they have the same length, Q and Q' coincide. That is, Q lies on the circle with diameter OP.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rough Inclined Plane...
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: December 8th 2011, 03:27 PM
  2. forces on an inclined plane
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: February 11th 2011, 08:32 AM
  3. area of triangle in inclined plane
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: October 30th 2009, 08:08 AM
  4. Car on an inclined plane
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: March 21st 2009, 06:47 PM
  5. Inclined plane
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: February 20th 2008, 02:10 AM

Search Tags


/mathhelpforum @mathhelpforum