$A$ ball is rolled off along the edge of a horizontal table with velocity $4 \, m/s$. It hits the ground after time $0.4 \, s$. Which of the following are correct?

Two particles are projected from a tower in opposite directions horizontally with speed $10\,m/s$ each. At $t=1\,s$,match the following two columns.

Column $I$	Column $II$
$(A)$ Relative acceleration between two	$(p)$ $0$ $SI$ unit
$(B)$ Relative velocity between two	$(q)$ $5$ $SI$ unit
$(C)$ Horizontal distance between two	$(r)$ $10$ $SI$ unit
$(D)$ Vertical distance between two	$(s)$ $20$ $SI$ unit

$A$ particle moves along a parabolic path $y = 9x^2$ in such a way that the $x$-component of velocity remains constant and has a value of $\frac{1}{3} \; m/s$. The acceleration of the particle is $....... \; m/s^2$.

Consider the two statements related to circular motion in usual notations:
$A$. In uniform circular motion,$\vec{\omega}$,$\vec{v}$,and $\vec{a}$ are always mutually perpendicular.
$B$. In non-uniform circular motion,$\vec{\omega}$,$\vec{v}$,and $\vec{a}$ are always mutually perpendicular.

The angle of projection of a particle is measured from the vertical axis as $\phi$ and the maximum height reached by the particle is $h_m$. Here $h_m$ as a function of $\phi$ can be represented as:

As shown in the figure,there is a spring-block system. $A$ block of mass $500\,g$ is pressed against a horizontal spring fixed at one end to compress the spring by $5.0\,cm$. The spring constant is $500\,N/m$. When released,calculate the horizontal distance from the edge of the table where it will hit the ground $4\,m$ below the spring. $(g = 10\,m/s^2)$