Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : When a body is projected at an angle $$45^{\circ}$$, it's range is maximum.

Reason R : For maximum range, the value of $$\sin 2 \theta$$ should be equal to one.

In the light of the above statements, choose the correct answer from the options given below:

A child stands on the edge of the cliff $$10 \mathrm{~m}$$ above the ground and throws a stone horizontally with an initial speed of $$5 \mathrm{~ms}^{-1}$$. Neglecting the air resistance, the speed with which the stone hits the ground will be $$\mathrm{ms}^{-1}$$ (given, $$g=10 \mathrm{~ms}^{-2}$$ ).

The initial speed of a projectile fired from ground is $$\mathrm{u}$$. At the highest point during its motion, the speed of projectile is $$\frac{\sqrt{3}}{2} u$$. The time of flight of the projectile is :

Two objects are projected with same velocity 'u' however at different angles $$\alpha$$ and $$\beta$$ with the horizontal. If $$\alpha+\beta=90^\circ$$, the ratio of horizontal range of the first object to the 2nd object will be :