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

$A$ hiker stands on the edge of a cliff $490 \ m$ above the ground and throws a stone horizontally with an initial speed of $15 \ m \ s^{-1}$. The speed with which it hits the ground is (in $m \ s^{-1}$)

$A$ ball is projected from a point $O$ as shown in the figure. It will strike the ground after ........ $s$ $\left(g=10 \, m/s^2\right)$.

Two balls are thrown horizontally from the top of a tower with velocities $v_1$ and $v_2$ in opposite directions at the same time. After how much time will the angle between the velocities of the balls become $90^o$?

Which of the following is the altitude-time graph for a projectile thrown horizontally from the top of a tower?