How to make vector from azimuth and speed?

Question

I don't know how to make $3$D vector of speed from azimuth and speed.

Azimuth is in degree and speed is in m/s.

Azimuth is angle on $X$ and $Y$.

Thank you for your help!

Answer 1

In spherical polar coordinates:

$\mathbf{v}= \dot{r} \mathbf{e}_{r}+ r\dot{\theta} \mathbf{e}_{\theta}+ r\dot{\phi} \sin \theta \mathbf{e}_{\phi}$

If the motion is confined in $xy$-plane, then $\theta=\frac{\pi}{2}$ and $\dot{\theta}=0$.

Thus, $\mathbf{v}=\dot{r} \mathbf{e}_{r}+r\dot{\phi} \mathbf{e}_{\phi}$