A student skates up a ramp that makes an angle $$30^\circ$$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed $$𝑣_0$$ and wants to turn around over a semicircular path xyz of radius 𝑅 during which he/she reaches a maximum height ℎ (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)