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Confused vectors in mechanics watch

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    An aircraft has a speed of 135 km/h in still air. It is flying northwards, so that it is at all times directly above a north/south highway. A ground observer tells the pilot by radio that a 70 km/h wind is blowing but neglects to tell him the wind direction. The pilot observes that in spite of the wind he can travel 135km along the highway in one hour.

    What are the direction of the wind and the heading of the plane (angle between its axis and the highway?)

    My answer: I resolved the plane's motion into vector components (please see attached) and solved. Please attempt the problem before looking at my diagram. I would like to know if our answers/method correlate as I think there are at least two ways to solve this problem (i.t.o. planes, excuse the pun)not to mention a purely inferential alternative, which would make my head spin.

    Thanks for the help.

    My answers are North, 63.6 degrees (angle of elevation).
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    Here's that diagram :facepalm:
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    (Original post by Everybody)
    Here's that diagram
    Well, that's a very original approach, I have to admit To make the plane fly upwards. It seems correct to me with the reservation that in your drawing the leg of the triangle shouldn't be labelled x+70 but just x. The rest seems correct, however I haven't looked into numbers.

    However, I believe that the more standard approach would be to make the plane move horizontally. This could be attained in such a way that the east-west components of the plane's and wind's velocities would cancel out each other, and the combination of the north-south components of their velocities would give the resultant velocity of 135\mathrm{\: km/h}.
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    I see, thanks (so the plane would travel with a slant? Assuming horizontal motion.)
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    The question is about bearings. The plane heads north east or north west (at 135km/hr) and that, combined with the wind's speed (70), allows it to travel due north at 135km/hr.
    Like this (try it before you click)
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    (Original post by Everybody)
    I see, thanks (so the plane would travel with a slant? Assuming horizontal motion.)
    Quite right More precisely, its head would be directed with a slant but the plane itself would move exactly in the north-south direction.
 
 
 
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Updated: March 21, 2011
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