Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

application about ellipses

Announcements Posted on
Talking about ISA/EMPA specifics is against our guidelines - read more here 05-03-2015
  1. Offline

    ReputationRep:
    the arch of a bridge spanning a canal is in the shape of the top half of an ellipse whose major axis is horizontal. the base of the archis 16m wide, and the heighest part of the arch is 4m above the canal. determine if a flat-topped barge 6m wide and 3.6m high can safely pass under the bridge.
  2. Offline

    ReputationRep:
    (Original post by ronnie)
    the arch of a bridge spanning a canal is in the shape of the top half of an ellipse whose major axis is horizontal. the base of the archis 16m wide, and the heighest part of the arch is 4m above the canal. determine if a flat-topped barge 6m wide and 3.6m high can safely pass under the bridge.
    The equation of the ellipse is (with the origin in the middle of the major axis)

    x^2/8^2 + y^2/4^2 = 1

    as the ellipse goes through (8,0) and (0,4).

    When y = 3.6 then

    x^2/64 = 1 - 3.6^2/16 = 0.19

    x^2 = 12.16

    x = 3.487...

    So the width under the bridge at height 3.6 is 2 x 3.487 = 6.974... which is comfortably enough to accommodate the width of 6.
  3. Offline

    ReputationRep:
    (Original post by RichE)
    The equation of the ellipse is (with the origin in the middle of the major axis)

    x^2/8^2 + y^2/4^2 = 1

    as the ellipse goes through (8,0) and (0,4).

    When y = 3.6 then

    x^2/64 = 1 - 3.6^2/16 = 0.19

    x^2 = 12.16

    x = 3.487...

    So the width under the bridge at height 3.6 is 2 x 3.487 = 6.974... which is comfortably enough to accommodate the width of 6.
    Yup that's right!
Updated: August 11, 2005
2015 general election
New on TSR

Loved by Students

Our big survey results unveiled

Article updates
Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.