Pilot flying in crosswind at 140 km/h, wind from northwest

[lankan911]

A pilot flies at 140 km/h. The heading is due East for 1 hour,due South for 1 hour, due west for 1 hour and due north for 1 hour. IF a steady wind blows at 60 km/h, how long and at what heading must he fly to return to the start point?

The wind is blowing in a northwest direction

 

[Tide]

Do you think it would help to know the direction of the wind?

 

[BobG]

You set this up so you can add vector components. For example, if East is the positive x and North is the positive y, your first leg is:

(140,0) km + (-42.4,42.4) km

You find the x component by multiplying the magnitude by the cosine of the heading. 'x' is always your principle axis (unless the problem specifically states otherwise). All your angles are measured from your principal axis. North would be positive 90 degrees, with North West being another 45 degrees past North. You find the y component by multiplying the magnitude by the sine of the heading.

Set each leg up like this. It's definitely to your advantage to keep the wind component separate from the plane's desired heading for each leg. (In fact, you could keep the wind in polar coordinates, NW at 60 km/h, until the very end if you wanted to and add them in last).