$A$ swimmer dived off a cliff with a running horizontal leap. What must his minimum speed be just as he leaves the top of the cliff so that he will miss the edge at the bottom,given that the ledge at the bottom is $2 \ m$ wide and $10 \ m$ below the top of the cliff?

$A$ ball rolls off the top of a stairway with horizontal velocity $u$. The steps are $0.1 \ m$ high and $0.1 \ m$ wide. The minimum velocity $u$ with which the ball just hits the $5^{\text{th}}$ step of the stairway will be $\sqrt{x} \ ms^{-1}$ where $x=$ . . . . . . [use $g=10 \ ms^{-2}$].

$A$ gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is $6.4 \text{ m}$. The speed of the bullets from the gun is . . . . . . m/s. (take $g = 10 \text{ m/s}^2$)

$A$ ball is thrown from a point with a speed $v_0$ at an angle of projection $\theta$. From the same point and at the same instant,a person starts running with a constant speed $v_0/2$ to catch the ball. Will the person be able to catch the ball? If yes,what should be the angle of projection?

$A$ stone is projected at an angle of $30^{\circ}$ to the horizontal. The ratio of the kinetic energy of the stone at the point of projection to its kinetic energy at the highest point of its flight will be:

If a body is projected with an angle $\theta$ to the horizontal, then