From the top of a tower of height $40\,m$,a ball is projected upwards with a speed of $20\,m/s$ at an angle of elevation of $30^{\circ}$. The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (take $g=10\,m/s^2$).

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

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 $g = 10 \text{ m/s}^2$)

$A$ man runs across the roof of a tall building and jumps horizontally with the hope of landing on the roof of the next building,which is at a lower height than the first. If his speed is $9 \, m/s$,the horizontal distance between the two buildings is $10 \, m$,and the height difference is $9 \, m$,will he be able to land on the next building? (Take $g = 10 \, m/s^2$)

$A$ body is projected horizontally from the top of a tower of height $180 \ m$ with a velocity of $20 \ ms^{-1}$. If acceleration due to gravity is $10 \ ms^{-2}$,then match the following:

List-$I$ (Kinematic Variable)	List-$II$ (Value)
$A$. Velocity of the body after $1 \ s$ (in $ms^{-1}$)	$I$. $5$
$B$. Horizontal displacement of the body after $1 \ s$ (in $m$)	$II$. $20$
$C$. Vertical displacement of the body after $1 \ s$ (in $m$)	$III$. $10$
$D$. Vertical velocity of the body after $1 \ s$ (in $ms^{-1}$)	$IV$. $22.4$

The correct answer is

$A$ ball of mass $0.2 \ kg$ is thrown from a height of $1 \ m$ with an initial velocity of $\sqrt{10} \ m/s$ at an angle of $45^{\circ}$ with the horizontal. Assuming acceleration due to gravity $g = 10 \ m/s^2$, the modulus of the momentum increment during the total time of motion in $kg \cdot m/s$ is: