Question

Rain is falling vertically with a speed of $35 \mathrm {~ms} ^ { - 1 }$ . Winds starts blowing after sometime with a speed of $12 \mathrm {~ms} ^ { - 1 }$in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

• A. $\sin ^ { - 1 } \left( \frac { 12 } { 35 } \right)$
• B. $\cos ^ { - 1 } \left( \frac { 12 } { 35 } \right)$
• C. $\tan ^ { - 1 } \left( \frac { 12 } { 35 } \right)$
• D. $\cot ^ { - 1 } \left( \frac { 12 } { 35 } \right)$

Answer 1

Answer: (C)

$\tan ^ { - 1 } \left( \frac { 12 } { 35 } \right)$

Answer 2

The velocity of the rain and the wind are represented by the vectors $\theta$is the angle which resultant velocity makes with the vertical.

Then