For a projectile, the ratio of maximum height reached to the square of flight time is ($g = 10 ms^{-2}$)

The maximum height attained by a projectile is increased by $10\,\%$ by increasing its speed of projection, without changing the angle of projection. The percentage increases in the horizontal range will be $...........\,\%$

$K_i :$ initial kinetic energy

$K_h :$ kinetic energy at the highest point

A particle is projected from the ground with velocity $u$ at angle $\theta$ with horizontal. The horizontal range, maximum height and time of flight are $R, H$ and $T$ respectively. They are given by $R = \frac{{{u^2}\sin 2\theta }}{g}$, $H = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}}$ and $T = \frac{{2u\sin \theta }}{g}$  Now keeping $u $ as fixed, $\theta$ is varied from $30^o$ to $60^o$. Then,

A ball is thrown from the ground to clear a wall $3\,m$ high at a distance of $6\,m$ and falls $18\,m$ away from the wall, the angle of projection of ball is

A stone projected at an angle of $60^o$ from the ground level strikes at an angle of $30^o$ on the roof of a building of height $‘h= 30\,m ’$ . Find the speed of projection(in $m/s$ ) of the stone