Two stones are projected horizontally from top of a tower in opposite directions with velocities $u_1$ and $u_2$. The time after which their displacement vectors are perpendicular to each other is

Question

$$(a)\;\frac{\sqrt {u_1}}{g}\quad (b)\;\frac{\sqrt {u_2}}{g} \quad (c)\;\frac{\sqrt {u_1u_2}}{g} \quad (d)\;\frac{2 \sqrt {u_1u_2}}{g}$$