Answer :
Given
The engines of a plane are pushing it due north at a rate of 300 mph, and the wind is pushing the plane 20° west of north at a rate of 40 mph.
To find the magnitude of the resultant vector.
Explanation:
It is given that,
Then,
[tex]\begin{gathered} Plane:300(\cos90\degree,\sin90\degree) \\ Wind:40(\cos110\degree,\sin110\degree) \end{gathered}[/tex]That implies,
[tex]\begin{gathered} Plane:300(0,1)=(0,300) \\ Wind:40(-0.34,0.94)=(-13.6,37.59) \end{gathered}[/tex]Adding these two points implies,
[tex]\begin{gathered} R=(0-13.6,300+37.59) \\ =(-13.6,337.6) \\ \Rightarrow|R|=\sqrt{(-13.6)^2+(337.6)^2} \\ =\sqrt{184.96+113973.76} \\ =\sqrt{114158.72} \\ =337.87 \\ =337.9mph \end{gathered}[/tex]Hence, the magnitude of R is 337.9mph.
