A roller$-$coaster car is released from rest at the top of the first rise and then moves freely with negligible friction. The roller coaster shown in Figure has a circular loop of radius $R$ in a vertical plane.

a$)$ Find the required height of the incline in terms of $R$ in order to avoid from dropping the car from the point B$.$

b$)$ If $h=(\frac{7}{2})R$ and $R=20m,$ find the speed, centripetal acceleration and tangential acceleration of the car at point $C.$