Question

An airplane is traveling at a speed of 200 miles/hour with a bearing of 240°. The wind velocity is 60 miles/hour at a bearing of 25°. What are the plane's actual speed and direction angle?

Answer 1

This is a vector problem so we will split it by components and add them.

x direction

200sin(240) + 60sin(25) = -147.847985

y direction

200cos(240) + 60cos(25) = -45.6215327

To find the actual speed we now find the magnitude

(-147.847985)^2 + (-45.6215327)^2 = c^2

c = 154.72669748 mph

To find the direction we can do arctan of the different directions:

arctan(-147.847985/-45.6215327) = 252.85 degrees.

So the plane is going 154.73 mph at 252.85 degrees :)