Answer
$261 \ m/s$
Work Step by Step
We create a right triangle, with one side being the plane's velocity and actual velocity and the other side being the plane's speed. Thus, we find the plane's actual velocity first:
$\frac{1500}{1.67}=900 \ km/h$
We now find the components of the plane's $1000 \ km/h$ velocity:
$v_x=1000cos(15^{\circ})=965.93 \ km/h $
$v_y = 1000sin(15^{\circ})=258.81 \ km/h$
Thus, we find the wind's speed:
$v=\sqrt{(258.81)^2+(1000-965.93)^2}=261 \ m/s$
