Question
A pilot flies a plane at a speed of 600 km/h with respect to the surrounding air. A wind is blowing to the northeast at a speed of 100 km/h. In what direction must the plane be aimed so that the resulting direction of the plane is due north?
Answers
bobpursley
Graphically this is so easy, and that is exactly how pilots would do it.
Put the wind at 100 NE, then on the end of that, take a vector from that point 600 in length, use a compass to draw an arc until it intercepts N. Then that is the direction.
Want to do it analytically?
You have the wind giving a 70.7km/h push to the East, so the plane must cancel that with a 70.7 W component.
so 70.7=600sinTheta (theta measured from N).
sinTheta= 70.7/600
theta= aresin (above) WEST of N
Put the wind at 100 NE, then on the end of that, take a vector from that point 600 in length, use a compass to draw an arc until it intercepts N. Then that is the direction.
Want to do it analytically?
You have the wind giving a 70.7km/h push to the East, so the plane must cancel that with a 70.7 W component.
so 70.7=600sinTheta (theta measured from N).
sinTheta= 70.7/600
theta= aresin (above) WEST of N