The greatest height to which a man can throw a stone is $h$. The greatest distance to which he can throw it, will be

A football player throws a ball with a velocity of $50$ metre/sec at an angle $30 $ degrees from the horizontal. The ball remains in the air for  ...... $\sec$ $(g = 10\,m/{s^2})$

A boy throws a ball with a velocity $u$ at an angle $\theta$ with the horizontal. At the same instant he starts running with uniform velocity to catch the ball before if hits the ground. To achieve this he should run with a velocity of

A grasshopper can jump maximum distance $1.6\; m$. It negligible time of the ground. How far can it go in $10 \;s$?

Given below are two statements. One is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion A :Two identical balls $A$ and $B$ thrown with same velocity '$u$ ' at two different angles with horizontal attained the same range $R$. If $A$ and $B$ reached the maximum height $h_{1}$ and $h_{2}$ respectively, then $R =4 \sqrt{ h _{1} h _{2}}$

Reason R: Product of said heights.

$h _{1} h _{2}=\left(\frac{u^{2} \sin ^{2} \theta}{2 g }\right) \cdot\left(\frac{u^{2} \cos ^{2} \theta}{2 g }\right)$

Choose the $CORRECT$ answer 

The velocity at the maximum height of a projectile is $\frac{\sqrt{3}}{2}$ times its initial velocity of projection $(u)$. Its range on the horizontal plane is .............