Question

A plane wants to fly 60 degrees north of west at 200 mph. The wind is blowing 10 mph directly north. What angle should the plane point at in order to travel along its preferred path?

Answer 1

58.5° north of west

Step-by-step explanation:

The the velocity of the plane relative to the wind + the velocity of the wind relative to the earth = the velocity of the plane relative to the earth.

`v_(plane|wind)+v_(wind|earth)=v_(plane|earth)`

Draw a picture of the vectors, then add the components.

In the x direction:

v cos θ + 0 = 200 cos 60

v cos θ = 100

In the y direction:

v sin θ + 10 = 200 sin 60

v sin θ = 163.2

Divide the second equation by the first equation:

tan θ = 1.632

θ = 58.5°

The plane should fly 58.5° north of west.