$(7$ pts$)$ A pilot flies a plane $(P)600km$ due north and arrives in $2\mathrm{.}0$ hours. The plane has a velocity relative to air $(A)$ of magnitude $v_{PA}=400k\frac{m}{h}$ which is directed $70\mathrm{.}0$ north of east. What is the magnitude $v_{AG}$ of the air relative to the ground $(G)?$

A$)156\mathrm{.}4k\frac{m}{h}$

B$)220\mathrm{.}9k\frac{m}{h}$

C$)52\mathrm{.}6k\frac{m}{h}$

D$)176\mathrm{.}5k\frac{m}{h}$

E$)128\mathrm{.}9k\frac{m}{h}$