We are building a road, and at one place we need to make a turn with a radius of 25m. The coefficient of static friction between the rubber and the material we are using is 0.6.
(a) Assuming that the road is flat through the turn, what is the maximum speed a car could have and safely navigate the turn without sliding off the road?
(b) Instead of keeping the road flat, let's bank the turn a little bit, giving the road an angle of 20° above the horizontal. With the banked turn, what is the maximum speed a car could have and still make it around the turn without sliding?