An airplane is heading N 10 degrees E at 260 mph. A 16 mph wind blows from the W. Find the plane's resultant velocity and direction. Use vector method

Hello!

Let the x-axis be from W to E and the y-axis from S to N. Then the own velocity of an airplane is represented by the vector

`V_1=lt260*sin(10^o),260*cos(10^o)gt`  (in mph).

The wind velocity is represented by the vector

`V_2=lt16,0gt`  ("blows from the W" means "to the E").

The combined velocity is

`V=V_1+V_2=<x_0,y_0> =`

`=lt260*sin(10^o)+16,260*cos(10^o)gt approx lt61.15,256.05gt.`

The magnitude of V (the speed) is `sqrt(x_0^2+y_0^2) approx263.25` (mph).

The direction is `arctan(y_0/x_0) approx76.57^o,` which means `90^o-76.57^o=13.43^o` "N to the E".

The answer: the speed is about 263.25 mph, the direction is about N 13.43 degrees E.