Calculate bearing from lateral and longitudinal speeds

Question

How can I calculate the bearing from an relative "origin" by lateral and longitudinal speeds?

For example if the lateral speed was 0 meters a second and the longitudinal speed is positive, that would mean the bearing would be 0 degrees of "origin" but if the longitudinal speed was negative that would indicate the bearing is 180 degrees of "origin". This scenario is simple. (I think, laughs at self).

Now lets make things interesting. The longitudinal speed is still positive, say 30.0 meters a second and my lateral speed is -0.05 meters a second. That would indicate my bearing would be angled ever so slightly "left of origin". But specifically what degree?

Is there a formula to calculate the bearing from two speeds?

Thanks!

Answer 1

After digging into the trigonometry trenches. I found a solution.

Given a lon/lat speeds create a 90 degree triangle. In this scenario the hypotenuse doesn't matter.

It boils down to (in python for folks)...

fraction = a / b # sides of the projection that form the 90 degree angle
if b < 0:
    fraction = b / a
bearing = 360 - (90 + math.atan(fraction))

Using that bearing. If you have a distance you can project a point.