The surface of a hill inclined at an angle $30^{\circ}$ to the horizontal. A stone is thrown from the summit of the hill (point $A$ ) at an initial speed $10 \mathrm{~m} / \mathrm{s}$ at angle $60^{\circ}$ to the vertical. If the stone strikes the hill at point $B$ as shown in the figure, the distance between $A$ and $B$ is (take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

Statement I An object subjected to velocities $\mathbf{v}_1$ and $\mathbf{v}_2$ has a resultant velocity with magnitude $|\mathbf{v}|=\left|\mathbf{v}_1\right|+\left|\mathbf{v}_2\right|$.

Statement II The magnitude of displacement is either less or equal to the path length of an object between two points.

Statement III The instantaeous acceleration is the limiting value of the average acceleration as the time interval approaches zero.

Which of the following is correct?

For a projectile, if $\alpha$ is the angle of projection, $R$ is the range, $h$ is the maximum height, $t$ is the time of flight then

Two cars, at a certain instant, are 50 km apart on a line running from south to north. The one farther north is moving west at $25 \mathrm{~km} / \mathrm{h}$. The other is moving towards north at $25 \mathrm{~km} / \mathrm{h}$. How long do they take to reach their distance of closest approach?