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Rain appears to fall vertically to a man...

Rain appears to fall vertically to a man walking at `3kmh^(-1)`, but when he changes his speed to double, the rain appears to fall at `45^@` with vertical. Study the following statements and find which of them are correct.
i. Velocity of rain is `2 (sqrt3) kmh^(-1)`.
ii. The angle of fall of rain (with vertical) is `theta = tan^(-1)(1/(sqrt2)).`
iii. The angle of fall of rain (with vertical) is `theta = sin^(-1) (1/(sqrt2))`.
iv. Velocity of rain is `3(sqrt2)kmh^(-1)` .

A

Statements (i) and (ii) are correct.

B

Statements (i) and (iii) are correct.

C

Statements (iii) and (iv) are correct.

D

Statements (ii) and (iv) are correct.

Text Solution

Verified by Experts

The correct Answer is:
C
c. Case I: Let `OP = 3hati` be the velocity of
man. `vec(OQ)` be the velocity of rain.
PQ is the velocity of rain relative to
man.

Case II: `vec(OR) = 6hati` is the new velocity
of man.
`vec(RQ)` = new velocity of rain relative to man
`OP = PR = PQ = 3`
Now `OQ^2 = OP^2 + PQ^2`, i.e., `OQ^2 = 3^2 + 3^2`
i.e., `OQ = 3sqrt(2) kmh^(-1)`
and `tan theta = (PQ)/(OP) = 3/3 = 1, i.e., theta = 45^@`.
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