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 $30^{\circ}$ to the horizontal. The ball will hit the ground in time ........ $s$ (Take $g = 10 \ m/s^2$)

$A$ 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:

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 $g=10\,m/s^2$).

Water is flowing from a horizontal pipe fixed at a height of $2\,m$ from the ground. If it falls at a horizontal distance of $3\,m$ as shown in the figure,the speed of water when it leaves the pipe is $............\,ms^{-1}$ (take $g=9.8\,ms^{-2}$).

From a tower of height $h$,one ball is thrown downwards with a velocity $u$ and another ball is thrown horizontally with the same velocity $u$. What is the ratio of their velocities when they reach the ground?

$A$ small object slides down with initial velocity equal to zero from the top of a smooth hill of height $H$. The other end of the hill is horizontal and is at height $\frac{H}{2}$ as shown in the figure. The horizontal distance covered by the object from the end of the hill to the ground is