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Rain appears to fall vertically to a man walking at \( 3 \mathrm{~km} \mathrm{~h}^{-1} \), but when he changes his speed to double, the rain appears to fall at \( 45^{\circ} \) with vertical. Study the following statements and find which of them are correct.
i. Velocity of rain is \( 2 \sqrt{3} \mathrm{~km} \mathrm{~h}^{-1} \)
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 \( 3 \sqrt{2} \mathrm{kmb}^{-1} \).
(1) Statements (i) and (ii) are correct.
(2) Statements (i) and (iii) are correct.
(3) Statements (iii) and (iv) are correct.
(4) Statements (ii) and (iv) are correct.
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