How Should a Plane Adjust Its Course in Crosswinds to Fly Due North?

[greyradio]

A plane is flying at a speed of 206 km/h in still air. There is a wind blowing at a speed of 76.6 km/h at 48.7 degrees to the east of north, and the pilot wishes to fly due north.

What angle should the plane fly? (assume the angle is measured between the plane and north.)
What speed does the plane fly relative to the ground with the wind blowing?I've tried drawing the vector diagram but I'm having trouble with it. I initially assumed the plane would be flying in a straight line from west to east. However, quickly realized that this created a right triangle where the hypotenuse is 76.6 km/h which is not possible as the largest vector is 206 km/h. My other attempts to solve it have failed. I was hoping someone could help me out. Thanks.

 

[member 553083]

The angle that the plane should fly is 48.7 degrees east of north. The speed of the plane relative to the ground with the wind blowing is 166 km/h.To solve this problem, you can draw a vector diagram. The vector for the plane's speed is 206 km/h at 0 degrees (due north). The vector for the wind is 76.6 km/h at 48.7 degrees (east of north). To find the total vector, add these two vectors together to get 166 km/h at 48.7 degrees. This is the direction and speed the plane should fly relative to the ground with the wind blowing. Therefore, the angle the plane should fly is 48.7 degrees east of north.