Answer:
1546.1 mph
Explanation:
Let's take the east direction as positive x-direction and north as positive y-direction.
The components of the initial velocity of the jet are:
[tex]v_x = 858 mph\\v_y = 0[/tex]
while the components of the wind's velocity are
[tex]a_x = (777)(cos 38^{\circ})=612.2 mph\\a_y = (777)(sin 38^{\circ})=478.4 mph[/tex]
So, the components of the new velocity of the jet are:
[tex]v'_x = v_x + a_x = 858+612.2 =1470.2 mph\\v'_y = v_y+a_y = 0+478.4=478.4 mph[/tex]
And therefore, the new speed is the magnitude of the new velocity, so:
[tex]v'=\sqrt{v'_x^2+v'_y^2 }=\sqrt{(1470.2)^2+(478.4)^2}=1546.1 mph[/tex]
