Rain appears is fall vertically to a man walking at 3 km h^-1, but when he changes his speed to double, the rain appears to fall at 45^o with vertical. Study the following statements and find which of them are correct

i. Velocify of rain is $2\sqrt{3}{\mathrm{kmh}}^{-1}$

ii. The angle of fall of rain (with vertical) is $\theta ={\tan }^{-1}\left(\frac{1}{\sqrt{2}}\right)$

iii. The angle of fall of rain (with vertical) is $\theta ={\sin }^{-1}\left(\frac{1}{\sqrt{2}}\right)$

iv. Velocity of rain is $3\sqrt{2}{\mathrm{kmh}}^{-1}$