Answer:I’m pretty sure I got this one right too
Step-by-step explanation:
The actual speed of the airplane is 472.56 mph in the direction of 41.57° north of west.
"In a two-dimensional coordinate system, any vector can be broken into x -component and y -component according to axis."
We can assume, east as the positive x- axis and north as the positive y-axis, respectively.
Similarly, west as the negative x- and south as the negative y-axis, respectively.
Therefore, the x- and y-components of the speeds.
Now, for the airplane:
x-component: - 500 × cos(45°) mph = - 353.55 mph
y-component: 500 × sin(45°) mph = 353.55 mph
For the wind:
y-component: -40 mph
Therefore, sum of the x-components = -353.55 mph
Similarly, sum of the y-components = (353.55 - 40) mph = 313.55 mph
Now, the actual speed =
[tex]\sqrt{(-353.55)^{2} + (313.55)^{2}}[/tex] mph
= [tex]\sqrt{223313.6}[/tex] mph
= 472.56 mph
Now, the direction of the airplane is:
tan(Ф) = [tex]\frac{313.55}{- 353.55}[/tex]
⇒ Ф = tan⁻¹( [tex]\frac{313.55}{- 353.55}[/tex])
⇒ Ф = - 41.57°
The actual speed of the airplane is 472.56 mph in the direction of 41.57° north of west.
Learn more about x and y-component of a vector here: https://brainly.com/question/15637558
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