A roller coaster has a small vertical loop with the lowest point 5 meters above the ground. The initial elevation from which the cart was released is 62.5 m. What should be radius of that loop to make sure the vertical acceleration at the bottom point does not exceed 2g?

magnityde and direction

this is a good question! i'll do some research and come back when i have the answer!

i think the answer is a, hope this : )

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft