5.46. a)
This time, lets take the x and y axes to be in the directions of the centripital acceleration and gravitational force respectively. Then summing the forces in the x direction (along the direction of the centripital acceleration) with the assumption that the car is just about to slip down the plane yields
Summing the forces in the y direction yields
Now, if we divide equation our equation for the forces in the x direction by the equation for the forces in the y direction, then we find
which corresponds to
If the car slips up the plane then the frictional force is in the opposite direction, so the sum of the forces in the x direction yields
meanwhile, the sum of the forces in the y direction is
Dividing these two equations as we did for the friction in the
opposite direction, we find that our equation for 
is
Parts b and c of the problem are identical to the other solution method.