A particle is thrown with a speed $$v$$ from a point $$O$$ at an angle $$\theta$$ with the horizontal plane such that it passes through the point $$P$$ at a height of $$1\,\mathrm{m}$$ and horizontal distance of $$5\,\mathrm{m}$$ from $$O$$, as shown in the figure. If acceleration due to gravity is $$g\,\mathrm{ms^{-2}}$$, then the correct statement(s) is(are):

A

If $$\theta=45^\circ$$, then $$v=\dfrac{5\sqrt{g}}{2}\,\mathrm{ms^{-1}}$$.

B

If $$\theta=45^\circ$$, the particle reaches its maximum height before it reaches $$P$$.

C

If $$\theta=30^\circ$$, the particle reaches its maximum height after reaching $$P$$.

D

If $$\theta=\tan^{-1}\!\left(\dfrac{1}{5}\right)$$, then $$v=125\sqrt{g}\,\mathrm{ms^{-1}}$$.