Question

A plane takes off heading west at a ground velocity of 500kph and climbing at an angle of 8 degrees. A 15kph wind is blowing from the north. Determine the resultant air and ground velocities. (sketch and label a diagram)

Answer 1

The plane is heading west (180 degrees) and climbing at an angle of 8 degrees, so its vector is [500kph, 172 degrees]. The wind is blowing from the north, going south, so its vector is [15kph, 270 degrees]. Find H=500cos172+15cos270 and V=500sin172+15sin270. The resultant vector's magnitude is \[\sqrt{H^2 \div V^2}\] and its direction is \[\tan^{-1} (V \div H)\] (Add 180 to the direction if H<0). To draw it, draw the plane vector then draw the wind vector from the tip of it (adding vector is always tip-to-tail) then draw the resultant vector.

Answer 2

Thanks SO much! :D

Answer 3

wait is it 172 degrees as in from the ground?

Answer 4

sorry for the late response; it's 172 degrees from the east (0 degrees) or 8 degrees up from the ground going west.