10. Challenge: Planning

In order to plan a successful path through the course, Carla will need to choose between many possible trajectories. If she chooses trajectories with too much lateral (sideways) acceleration, she may slide off the track. Help Carla find the best trajectory by eliminating turns that are too sharp for her speed!

The equation for lateral acceleration (side to side acceleration) is given below.

a_{\text{lat}} = \frac{v^2}{R}

In junkyard conditions, the maximum lateral acceleration that Carla's tires can support is 12 m/s^2. If she's traveling at a velocity of 30 m/s, what's the sharpest turn (minimum turning radius) she can make?