The greatest height to which a man can throw a stone is $h$. The greatest distance to which he can throw it will be:

The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are $R_{1}, R_{2}$ and $H_{1}, H_{2}$ respectively. Choose the correct option:

$A$ particle has initial velocity $(2\hat{i} + 3\hat{j})$ and acceleration $(0.3\hat{i} + 0.2\hat{j})$. The magnitude of velocity after $10\, s$ will be:

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

$A$ cart moves with a constant speed along a horizontal circular path. From the cart,a particle is thrown up vertically with respect to the cart.

Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $\pi / 3$ and its maximum height is $h_1$,then the maximum height of the other will be: