Question

You are traveling on a hilly road. At a particular spot, when your car is perfectly horizontal, the road follows a circular arc of some unknown radius. Your speedometer reads 90.0 km/h, and your apparent weight is 30% larger than usual. Use g-9.80 m/s2 for this problem. (a) Are you at the bottom of a hill or the top of a hill at that instant? the bottom of a hill the top of a hill There's not enough information to decide. (b) What is the radius of the circular arc?

Answer 1

a) Option 1 the bottom of the hill.

Since we are going in a circular arc there must be one component in the net force we are experiencing which points towards the center of the circular arc and whose magnitude is mv^2/r. No horizontal force contributes to mv^2/r.  
The 30% heavier weight is actually just the magnitude of Fn. Since we feel heavier we may compare this to upward acceleration of the elevator. This means that we have some extra acceleration upward. This extra part must be the ac=v^2/r, therefore the center of the arc must be above our head
so we’re at the bottom of the hill.

b)
v = 90 km/h = 25 m/s

v^2/r = 0.30g

=> r = v^2/0.30g

=> r = (25)^2/(0.3*9.8)
=> r = 213m