A golfer stands on a flat beach at a distance $b$ from the foot of a cliff of height $h$, where $b>\sqrt{3h}$, and hits a golf ball of mass $m$ towards the cliff with an initial speed $v_{0}$ and an angle of projection $\frac{π} {6}$ above the horizontal.
(i) Neglecting air resistance, show that the cannon ball will clear the top of the cliff provided $$v_{0}^{2}>\frac{2gb^{2}}{\sqrt{3}(b-\sqrt{3h})}$$
(ii) Assuming that condition (1) holds and there is a large flat field at the top of the cliff, find the time at which the ball will hit the field, and show that the speed of the ball at this time is $$\sqrt{v_{0}^{2}-2gh}$$
Hint: $$ F = m (\ddot{x}, \ddot{y}) = (0, - m g) $$