Question

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?

Answer 1

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:

`Tan(\alpha )=(WindSpeed)/(PlaneSpeed)\\\\\alpha =Tan((WindSpeed)/(PlaneSpeed))^(-1)=ArcTan((WindSpeed)/(PlaneSpeed))\\\\\alpha =ArcTan((WindSpeed)/(PlaneSpeed))`

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

`Wind=75(km)/(m) (southward)\\\\Airplane=310(km)/(h)`

`\alpha =ArcTan((WindSpeed)/(PlaneSpeed))\\\\\alpha =(75(km)/(h) )/(310(km)/(h) )=13.6\°`

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

Have a nice day!