A frictionless roller coaster is given an initial velocity of Vo at height h = 12 m. The radius of curvature of the track at point A is R = 35 m. Find the maximum value of Vo so that the roller coaster stays on the track at A solely because of gravity. The acceleration due to gravity is 9.8 m/s^2. Fine the value of h' that is necessary if the roller coaster just makes it to point B. I just need the answer to the last part of the problem (height of h'...I have already found Vo to be 16.2665

Question

A frictionless roller coaster is given an initial velocity of Vo at height h = 12 m.  The radius of curvature of the track at point A is R = 35 m.  Find the maximum value of Vo so that the roller coaster stays on the track at A solely because of gravity.  The acceleration due to gravity is  9.8 m/s^2.  Fine the value of h' that is necessary if the roller coaster just makes it to point B.  I just need the answer to the last part of the problem (height of h'...I have already found Vo to be 16.2665

anonymous · Answer

If the coaster is upside down at A, then need 

v^2 / R = g = 9.8 m/s^2 to just match gravity

The additional height h' gained from the initial velocity is obtained from

0.5 Vo^2 = g h' [kinetic energy changed to potential energy]

anonymous · Answer

the roller coaster is not upside down at point A

anonymous · Answer

attachment