The angle of a banked road

Road builders bank a bend so that cars at the design speed need no friction at all. You will make the program find the bank angle for a range of speeds on three bends, and the fastest design speed that a gentle bank allows.

The idea. At the design speed $v$, a bend of radius $r$ banked at $\theta$ needs no friction when

Your tasks.

1. Change the speeds from km/h to m/s.
2. Work out the bank angle, in degrees, for every speed on each bend.
3. Find the fastest design speed, in km/h, for the $150\ \text{m}$ bend if the bank may be at most $12^\circ$.