Answer:
966 mph
Explanation:
Using as convention:
- East --> positive x-direction
- North --> Positive y-direction
The x- and y- components of the initial velocity of the jet can be written as
[tex]v_{1x} = 406 mph\\v_{1y} = 0[/tex]
While the components of the velocity of the wind are
[tex]v_{2x} = (568)(cos 15^{\circ})=548.6 mph\\v_{2y} = (568)(sin 15^{\circ})=147.0 mph[/tex]
So the components of the resultant velocity of the jet are
[tex]v_x = v_{1x}+v_{2x}=406+548.6=954.6 mph\\v_y = v_{1y}+v_{2y}=0+147.0=147.0 mph[/tex]
And the new speed is the magnitude of the resultant velocity:
[tex]v=\sqrt{v_x^2+v_y^2}=\sqrt{(954.6)^2+(147.0)^2}=965.8 mph \sim 966 mph[/tex]
