Choose the correct formula for the horizontal range of an oblique projectile from a height from the following options.

Two posts of heights $20 \mathrm{m}$ and $10 \mathrm{m}$ are $60 \mathrm{m}$ apart, as shown in the figure. Foodgrains are continuously distributed between the two posts. A crow sitting on top of the taller post wants to pick up a grain and sit on the other post. What should be the distance of the grain it picks from the bottom of the taller post to minimise the total flight length?

A particle is projected with a velocity $v$ so that its range on a horizontal plane is twice the greatest height attained. Show that the range is $\frac{4v^2}{5g}$.

Two particles are simultaneously projected in the horizontal direction from a point $P$ at a certain height. The initial velocities of the particles are oppositely directed to each other and have magnitude $v$ each. The separation between the particles at a time when their position vectors (drawn from the point $P)$ are mutually perpendicular, is:

The velocity of a projectile at the initial point $A$ is $\left(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$. Its velocity (in $\mathrm{m} {\mathrm{s}}^{-1}$) at point $B$ is