A jet is flying through a wind that is blowing with a speed of $50m\frac{i}{h}$ in the direction $N30E($see the following figure$).$

i$)$

The jet has a speed of $770m\frac{i}{h}$ relative to the air, and the pilot heads the jet in the direction $N45E.($Assume that the i vector points east, and the $j$ vector points north.$)$

$($a$)$ Express the velocity of the wind as a vector in component form.

$($b$)$ Express the velocity of the jet relative to the air as a vector in component form.

$($c$)$ Find the true velocity of the jet as a vector. $($Round your answer to two decimal places.$)$

$($d$)$ Find the true speed of the jet $($in $m\frac{i}{h}).($Round your answer to the nearest integer.$)$

$m\frac{i}{h}$

Find the direction of the jet $($in degrees E of N$).($Round your answer to the nearest integer.$)$

N $-$ E