A 775 kg roller coaster car is at the top of a roller coaster car is at the top of a roller coaster as shown below. The height of the car at point A is the minimum height that is necessary for the car to stay on the loop. The radius of the loop is 30 m.

Question

What is the height of the car at point A?

Answer 1

g = v^2/r at top of loop
g = v^2/30
solve for v^2 = 30 *g

now the car drops A-2r to that point at the top of the loop
(1/2) m v^2 = m g (A-60)
v^2 = 2 g(A-60)
30 g = 2g (A-60 ) = 2 g A -120 g
150 g = 2gA
A = 75
check my arithmetic !

Answer 2

Note this does no depend on the mass (lucky or it would be different for skinny kids and fat adults), or even on g (independent of planet:)

Answer 3

check, drops 15 meters to top of loop
v^2 = 2 g (15)

needs v^2/30 = g

sure enough 2*15 g /30 = g