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Motion in a Plane, Vector Addition/Subtraction

  1. Sep 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Snoopy is flying his plane, the Sopwith Camel, in search of the Red Baron. He flies with a constant speed of 120 km/h relative to air, and makes instantaneous turns when necessary. He follows a perfectly square path on the ground, using north - south and east - west roads as a guide for each of the 60 km sides. On a day when there is a steady 60 km/h wind blowing diagonally across the square (southwest wind), how long does the trip take?

    2. Relevant equations
    Relative Motion
    V-speed, P-Plane, A-Air, G-Ground
    PVG = PVA + AVG

    Cosine Law

    3. The attempt at a solution
    My assumption on the problem is that the airspeed of 120 km/h must have an added components of 60 km/h (NE) to counteract it so that the resultant will have its course on the correct path 60 km North. This is done for each side.
    I have drawn out my vectors in the attached image.
    Using cosine law I can find the new airspeed, but I don't know what to do after.
    Please Help and Thank You
     

    Attached Files:

  2. jcsd
  3. Sep 23, 2011 #2

    PeterO

    User Avatar
    Homework Helper

    Your diagram will find a new ground speed if Snoopy points the plane due North, then "side-slips" his way across the landscape.
    Snoopy is to maintain a ground speed of due North, so on the first leg will be pointing somewhat West of North.

    The wind speed adds a constant North and East component to any velocity the plane has relative to the air.
    To fly in a specific N, S, E or W direction, the velocity of the plane must have a component to cancel out the "unwanted" component of the wind.

    For example, suppose a different wind had a North component of 20 km/h, and an East component of 20 km/h.

    To fly North, the 120km/h of the plane would have to have a westerly component of 20 km/h to balance the wind and achieve a due North heading.

    PS. Wouldn't it be weird if the problem could be worked out this simply:
    If there was no wind, Snoopy merely points N, E, S then W, and flies for 60km each time, to cover the square. That would take 2 hours.
    If he did that with the wind blowing, he would actually end up 120 km NE of where he started. It would take 2 hours to return to his starting point [he would be flying into a head wind so only gaining 60 k each hour]. So the whole trip would take 4 hours.
     
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