The velocity at the maximum height of a projectile is half of its initial velocity $u$. Its range on the horizontal plane is

Three identical balls are projected with the same speed at angles $30^{\circ}$,$45^{\circ}$,and $60^{\circ}$. Their ranges are $R_1$,$R_2$,and $R_3$ respectively. Then:

$A$ ball is projected at an angle $45^{\circ}$ with the horizontal. It passes through a wall of height $h$ at a horizontal distance $d_1$ from the point of projection and strikes the ground at a horizontal distance $(d_1 + d_2)$ from the point of projection. Then $h$ is:

The initial speed of a bullet fired from a rifle is $630 \; m/s$. The rifle is fired at the center of a target $700 \; m$ away at the same level as the target. How far above the center of the target (in $m$) must the rifle be aimed in order to hit the target? (Take $g = 10 \; m/s^2$)

$A$ ball can be thrown to a maximum horizontal distance of $100\,m$. To what maximum height can it be thrown?

$A$ projectile is thrown with velocity $u$ at an angle of $15^o$ and has a range $R$. What will be the range of the projectile if it is thrown with velocity $2u$ at an angle of $45^o$ (in $, R$)?