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Closest approach of two trains on perpendicular tracks

  1. Apr 22, 2005 #1
    Kinda confused on this one becuase of the time difference involved

    A train leaves a station going south at 60 km/hr at 10:00. Another train heading due west reaches this station at 11:00. The latter train was travelling at 45km/hr. At what time are they the closest?

    To start with the 45 train is 45km away from teh station and in the end the distnace is 60 km
    iformulated something like 45(1-t) + 60t = Distance
    but that doesnt yield the answer i need...
    can someone help!

    Attached Files:

  2. jcsd
  3. Apr 22, 2005 #2


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    Staff Emeritus
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    Call the point at which the 60 km/hr train starts the "origin." You know the direction and distance of each train from the origin at any given time.

    As shown in your figure, the vectors from the origin to each train form a right triangle, the hypotenuse of which is the distance between them.

    If you know the length of the triangle's legs as a function of time, use the Pythagorean formula to find the length of the triangle's hypotenuse as a function of time. Then, find the minimum of that function.

    - Warren
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