The figure shows a projectile thrown with a speed $u = 20 \, m/s$ at an angle of $30^{\circ}$ with the horizontal from the top of a building $40 \, m$ high. The horizontal range of the projectile is ........... $m$.

Three balls,$A, B$ and $C$ are released and all reach the point $X$ (shown in the figure). Balls $A$ and $B$ are released from two identical structures,one kept on the ground and the other at height $h$ from the ground as shown in the figure. They take time $t_A$ and $t_B$ respectively to reach $X$ (time starts after they leave the end of the horizontal portion of the structure). The ball $C$ is released from a point at height $h$,vertically above $X$ and reaches $X$ in time $t_C$. Choose the correct option.

$A$ body is projected horizontally with a velocity of $4\,m/s$ from the top of a high tower. The velocity of the body after $0.7\,s$ is nearly $.....\,m/s$ (take $g=10\,m/s^2$).

Two particles in the same vertical plane are thrown to strike at the same time. One is thrown from the ground and the other from a height $h$ vertically above it. The ground particle is thrown obliquely with speed $u$ at an angle $\theta$ and achieves a maximum height $H$. The second particle is thrown horizontally with the same speed $u$. What is the maximum height $h$ such that the two particles strike each other in the air?

An aeroplane is moving with horizontal velocity $u$ at height $h$. The velocity of a packet dropped from it on the earth's surface will be ($g$ is acceleration due to gravity).

$A$ bowling machine placed at a height $h$ above the earth's surface releases different balls with different angles but with the same velocity $10 \sqrt{3} \text{ m s}^{-1}$. All these balls' landing velocities make angles of $30^{\circ}$ or more with the horizontal. Find the height $h$ (in meters) (acceleration due to gravity $g = 10 \text{ m s}^{-2}$).