Physics (simple trig): a novice pilot sets a plane's controls, thinking that the plane will fly 250 km/hr to the north. If the wind blows at 75 km/hr to the south east (135 degrees), what is the plane's resultant velocity?
The velocity of the plane, the wind vector and the resultant plane velocity form a triangle. P = velocity vector of plane W = wind vector V = resultant plane velocity P + W = V You can calculate vector components of P and W and combine them to get V. Px = 0 ........................ Wx = 75cos(45) = (75/2)SQRT(2) Py = 250 ..................... Wy = -75sin(45) = -(75/2)SQRT(2) Vx = Px + Wx = 0 + (75/2)SQRT(2) = (75/2)SQRT(2) = 53.033 Vy = Py + Wy = 250 - (75/2)SQRT(2) = 196.970 A = Angle from north of resultant velocity tan(A) = Vx/Vy = 53.033/196.970 = 0.269248 A = 15.07 degrees v = Magnitude of resultant velocity = SQRT{(53.033)^2 + (196.970)^2] v = 203 km/h The resultant velocity is 203 km/h at an an angle of 15 degrees east of north.
