Question

The engines of a plane are pushing itdue north at a rate of 300 mph, andthe wind is pushing the plane 20°west of north at a rate of 40 mph.what is the magnitude of theresultant vector?[?] mphRound to the nearest tenth.

Answer 1

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,

$\begin{gathered} Plane:300(\cos90\degree,\sin90\degree) \\ Wind:40(\cos110\degree,\sin110\degree) \end{gathered}$

That implies,

$\begin{gathered} Plane:300(0,1)=(0,300) \\ Wind:40(-0.34,0.94)=(-13.6,37.59) \end{gathered}$

Adding these two points implies,

$\begin{gathered} R=(0-13.6,300+37.59) \\ =(-13.6,337.6) \\ \Rightarrow|R|=\sqrt{(-13.6)^2+(337.6)^2} \\ =\sqrt{184.96+113973.76} \\ =\sqrt{114158.72} \\ =337.87 \\ =337.9mph \end{gathered}$

Hence, the magnitude of R is 337.9mph.