A stone is projected from a point on ground at some angle of projection. At the same time, a bee starts from a point directly above this point of projection at a height of 2.5 m horizontally with speed $5\sqrt{2}{\mathrm{ms}}^{-1}$. It is found that the stone just touches the bee at one point. Find range of projectile motion of stone.

If the bee crosses the projectile other then at the maximum height point, it should cross the projectile twice.

Since it has been mentioned that the bee exactly touches the projectile once, the bee and the projectile meet at the maximum height point.

Here, $\mathrm{H}=\frac{{{\mathrm{u}}_{\mathrm{y}}}^2}{2\mathrm{g}}$

$\Rightarrow 2.5=\frac{{{\mathrm{u}}_{\mathrm{y}}}^2}{20}$

or ${\mathrm{u}}_{\mathrm{y}}=\sqrt{50}$

and $u_x=u=5\sqrt{2}$

$\therefore \mathrm{R}=\frac{2u_x{u}_y}{\mathrm{g}}=\frac{2\times \sqrt{50}\times 5\sqrt{2}}{10}=10\mathrm{m}$