Relative Velocity Problem

  • Thread starter greyradio
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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.
 
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