Question

An airplane is moving at 120m/s at an angle of 10 degree along x- axis , through a 30m/cross wind,blowing at angle of 260 degree with x-axis, determine the resultant velocity of the airplane.

Answer 1

Vpx = 120 * cos 10 = 118.2 x-component of airplane velocity

Vpy = 120 * sin 10 = 20.8 y-component of airplane velocity

Vwx = 30 cos 260 = -5.2 x-component of wind velocity

Vwy = 30 sin 260 = -29.5 y-component of wind velocity

Vx = 118.2 - 5.2 = 113 net ground x-component of plane velocity

Vy = 20.8 - 29.5 = -8.7 net ground y-component of plane velocity

V = (Vx^2 + Vy^2)^1/2 = 113.3 m/s

Caution: Wind direction is usually stated in terms of the direction

from which the wind is blowing (a NW wind means the wind is blowing

from the Northwest). If that is the meaning of the problem here then you have to reverse the signs of the wind speed components.