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To practice Problem-Solving Strategy 3.2 Relative velocity. An airplane pilot wishes to fly directly westward. According to the weather bureau, a wind of 75.0 km/hour is blowing southward. The speed of the plane relative to the air (called the "air speed") as measured by instruments aboard the plane is 310 km/hour . In which direction should the pilot head?

Respuesta :

mixter17

The pilot should head 13.6° north of west.

Why?

We can solve the problem by using trigonometric relations. Since there is a right triangle formed between the direction that the pilot wants to fly to and the wind's speed, we can use the following formula:

[tex]Tan(\alpha )=\frac{WindSpeed}{PlaneSpeed}\\\\\alpha =Tan(\frac{WindSpeed}{PlaneSpeed})^{-1}=ArcTan(\frac{WindSpeed}{PlaneSpeed})\\\\\alpha =ArcTan(\frac{WindSpeed}{PlaneSpeed})[/tex]

Now, substituting the given information and calculating, we have:

[tex]Wind=75\frac{km}{m} (southward)\\\\Airplane=310\frac{km}{h}[/tex]

[tex]\alpha =ArcTan(\frac{WindSpeed}{PlaneSpeed})\\\\\alpha =\frac{75\frac{km}{h} }{310\frac{km}{h} }=13.6\°[/tex]

Hence, we have that the pilot should head to 13.6° north of west.

Have a nice day!

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