Answer
Resultant velocity of the airplane is 203.96 miles per hour.
Work Step by Step
The model situation in plane $ \mathbb{R}^2$
$Unit \;vectotrs\; is\; \overrightarrow{a}\;=(1,0)\; from\;East\;\;\;\;\;\;\;and\;\;\;\;\;\;\overrightarrow{b}\;=(0,-1)\;from\;North\\\\$
When wind blows:
$200\;\overrightarrow{a}\;+\;40\;\overrightarrow{b}\;$
$=\;200(1,0)\;+\;40(0,-1)\;=\;(200,0)\;+\;(0,-40)\;=\;(200,-40)\\\\$
The velocity of the plane:
$\left \| 200\;\overrightarrow{a}\;+\;40\;\overrightarrow{b} \right \|\;=\;\sqrt{200^2\;+\;(-40)^2}\;=\;203.96\\\\$
Resultant velocity of the airplane is 203.96 miles per hour.
