A man running at a speed of 5 km/h , find that the rain falls vertically. When he stops running, he finds that the rain is falling at an angle of 60° with the horizontal. The velocity of rain with respect to running man is

Question

A man running at a speed of 5 km/h , find that the rain falls vertically. When he stops running, he finds that the rain is falling at an angle of 60° with the horizontal. The velocity of rain with respect to running man is (A)  (5/√3) km/h  (B)  (5√3/2) km/h  (C)  (4√3/2) km/h  (D)  5√3 km/h

Tardigrade Admin · Accepted Answer

Consider the situational diagram as shown below. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/05b70f71b91533ee30e00657ce0acb80-.png" /> In triangle O A P, tan 30°= (vm/vm) =( text Velocity of man / text Velocity of rain with respect to man ) ⇒ vI m =(5/1 / √3) =5 √3 km / h

Q. A man running at a speed of $5 km / h$ , find that the rain falls vertically. When he stops running, he finds that the rain is falling at an angle of $6 0^{\circ}$ with the horizontal. The velocity of rain with respect to running man is

$\frac{5}{3} km / h$

$\frac{5 3}{2} km / h$

$\frac{4 3}{2} km / h$

$53 km / h$

Consider the situational diagram as shown below.

In $△ O A P$ ,
$tan 3 0^{\circ} = \frac{v _{m}}{v _{m}}$
$= \frac{Velocity of man}{Velocity of rain with respect to man}$
$\Rightarrow v_{I m} = \frac{5}{1/ 3}$
$= 53 km / h$

Q. A man running at a speed of 5km/h , find that the rain falls vertically. When he stops running, he finds that the rain is falling at an angle of 60∘ with the horizontal. The velocity of rain with respect to running man is

3​5​km/h

253​​km/h

243​​km/h

53​km/h