Question

An aeroplane's compass indicates that it is headed due to North, and it airspeed indicator shows that is moving through the air at 24 0 km/h. If there is a 100 km/h wind from west to east. In what direction should the pilot head to travel due north? What will be her velocity relative to the earth?
compass heading T degrees east of north (it will be negative of course)

North component = 240 cos T
East component = 240 sin T + 100
we need ZERO east
so
240 sin T = -100
sin T = -0.4166666.....
T = -24.6 degrees which is 360 - 24.6 on the compass

speed north over ground = 240 cos 24.6

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