Question

Rain appears to fall vertically or a man walking at 3 kmh^-1 but if he doubles his speed to the rain appears to fall at 45^o. The real velocity of rain is

• A. 3√2 kmh^-1, 45^o
• B. 2√3 kmh^-1, 45^o
• C. 3√2 kmh^-1, 30^o
• D. 2√3 kmh^-1, 60^o

Answer 1

Answer: (A)

3√2 kmh^-1, 45^o

Answer 2

Here $\overset{\rightarrow}{OP}$ equal to 3$\widehat{i}$ is the velocity of man $\overset{\rightarrow}{OQ}$ is the velocity of rain.

∴ PQ is velocity of rain relative to man. In the second case, $\overset{\rightarrow}{OR}$ equal to 6$\widehat{i}$ is the new velocity of man and $\overset{\rightarrow}{RQ}$= new velocity of rain relative to man.

Now OQ² = OP² + PQ²

or OQ² = 3² + 3² ( PQ = PR = 6 – 3 = 3)

or OQ = 3√2 kmh^-1

tanθ = PQ/OQ = 3/3 = 1 or Q = 45^o