1. The problem statement, all variables and given/known data A car of mass m is initially stationary on a smooth track at distance h above the ground. What would be the minimum value of h required in order for the car to remain on the track throughout its journey around the loop of radius r? 2. Relevant equations KE(bottom)>PE (top) F=mv^/r 3. The attempt at a solution I solved this using the minimum velocty, sqrtgr, at the top and applying energy conservation. But I tried this using two other alternate approaches that didmn't yield the correct results: 1)KEbottom>PE(Top)= mv^2(.5)=mg(2r). This gives the minimum velocity as sqrt4gr. Although it should be sqrtgr according to centripetal force eq (mv^2/r=mg). 2) Second approach: I have attached the snap below of the solution.Now for h to be minimum, costheeta should be one. Why is it taken to be -1. Kindly resolve both of these queries.