Answer:
1546.2 mph
Explanation:
The new speed of the aircraft will be the magnitude of the resultant velocity due to the velocity of the aircraft + the velocity of the wind.
The components of the initial velocity of the jet are:
[tex]v_x = 858 mph\\v_y = 0[/tex]
where we took east as positive x-direction and north as positive y-direction.
The components of the wind's velocity are
[tex]v'_x = (777)(cos 38^{\circ})=612.3 mph\\v'_y = (777)(sin 38^{\circ})=478.4 mph[/tex]
So the components of the resultant velocity are
[tex]V_x = v_x + v'_x = 858+612.3=1470.3 mph\\V_y = v_y+v'_y = 0+478.4 = 478.4 mph[/tex]
And so, the new speed of the plane respect to the ground is
[tex]V=\sqrt{(1470.3)^2+(478.4)^2}=1546.2 mph[/tex]
