An archer shoots an arrow from a height of $4.2 \text{ m}$ above the ground with a speed of $40 \text{ m/s}$ at an angle of $30^{\circ}$ with the horizontal, as shown in the figure. Determine the total horizontal distance $R$ covered by the arrow when it hits the ground. (Take $g = 10 \text{ m/s}^2$)

$A$ bomber plane moves horizontally with a speed of $500 \ m/s$ and a bomb released from it strikes the ground in $10 \ s$. The angle with the horizontal at which it strikes the ground will be $(g = 10 \ m/s^2)$.

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?

$A$ 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 $g = 10 \text{ m s}^{-2}$).

Two balls of mass $M$ and $2M$ are thrown horizontally with the same initial velocity $v_{0}$ from the top of a tall tower and experience a drag force of $-kv$ $(k > 0)$,where $v$ is the instantaneous velocity. Then,

$A$ particle is dropped from a height of $20\,m$ onto horizontal ground. There is wind blowing,due to which the horizontal acceleration of the particle becomes $6\,ms^{-2}$. Find the horizontal displacement of the particle until it reaches the ground (in $m$).