Answer:
The correct option is A.
Step-by-step explanation:
The magnitude of a vector V=<a,b> is
[tex]|V|=\sqrt{a^2+b^2}[/tex]
It is given that a jet, in calm air conditions, travels with velocity vector (389, 389). The magnitude of this vector is
[tex]|V_1|=\sqrt{389^2+389^2}=389\sqrt{2}[/tex]
Since the x and y coordinates are same, therefore the angle with x-axis is 45 degrees or [tex]\frac{\pi}{2}[/tex].
The wind velocity (in mph) at the plane’s cruising altitude is given by (0, 50).
[tex]|V_2|=\sqrt{0^2+50^2}=50[/tex]
The formula for resultant vector of vectors having a and b is
[tex]R=\sqrt{a^2+b^2+2ab\cos \theta}[/tex]
[tex]R=\sqrt{(389\sqrt{2})^2+(50)^2+2(389\sqrt{2})(50)\cos (\frac{\pi}{4})}[/tex]
[tex]R=586.55[/tex]
[tex]R=587[/tex]
The true speed of the plane is 287 mph.
Therefor the correct option is A.
