A girl standing on a road holds her umbrella | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $\vec{V}_R$ be the velocity of rain with respect to the ground and $\vec{V}_G$ be the velocity of the girl with respect to the ground.When the

Vedclass · Accepted Answer

$\frac{30}{\sqrt{2}}$

Vedclass · Answer

(C) Let $\vec{V}_R$ be the velocity of rain with respect to the ground and $\vec{V}_G$ be the velocity of the girl with respect to the ground.When the girl is standing,she holds the umbrella at $45^{\circ}$ with the vertical,which means the direction of rain with respect to the ground makes an angle of $45^{\circ}$ with the vertical.From the vector triangle,$	an 45^{\circ} = \frac{|\vec{V}_G|}{|\vec{V}_{R,G}|}$,where $\vec{V}_{R,G}$ is the velocity of rain with respect to the girl.When the girl starts running with velocity $\vec{V}_G = 15 \sqrt{2} \; kmh^{-1}$,the rain hits her head vertically. This means the relative velocity of rain with respect to the girl,$\vec{V}_{R,G} = \vec{V}_R - \vec{V}_G$,is vertical.From the geometry of the velocity triangle,$|\vec{V}_{R,G}| = \frac{|\vec{V}_G|}{	an 45^{\circ}}$.Since $	an 45^{\circ} = 1$,we have $|\vec{V}_{R,G}| = |\vec{V}_G| = 15 \sqrt{2} \; kmh^{-1}$.The speed of rain drops with respect to the moving girl is $|\vec{V}_{R,G}| = 15 \sqrt{2} \; kmh^{-1}$.Wait,checking the options provided: $15 \sqrt{2} \approx 21.21$. None of the options match. Let's re-evaluate: If the rain hits her vertically when she runs,then $\vec{V}_{R,G}$ is vertical. The horizontal component of $\vec{V}_R$ must be equal to the girl's speed $V_G = 15 \sqrt{2}$.Thus,$V_R \sin 45^{\circ} = 15 \sqrt{2} \Rightarrow V_R \frac{1}{\sqrt{2}} = 15 \sqrt{2} \Rightarrow V_R = 30 \; kmh^{-1}$.The vertical component of rain is $V_{R,G} = V_R \cos 45^{\circ} = 30 	imes \frac{1}{\sqrt{2}} = \frac{30}{\sqrt{2}} \; kmh^{-1}$.Thus,the correct option is $C$.

Similar Questions

$A$ passenger sitting in a train $A$ moving at $90\,km/h$ observes another train $B$ moving in the opposite direction for $8\,s$. If the velocity of the train $B$ is $54\,km/h$,then the length of train $B$ is $..........\,m$.

$A$ man walking along a straight line with a velocity $6 \text{ km/h}$ encounters rain falling vertically down with a velocity $6\sqrt{3} \text{ km/h}$. At what angle should the man hold his umbrella to protect himself from the rain?

On a calm day,a boat can go across a lake and return in time $T_0$ at a speed $V$. On a rough day,there is a uniform current at speed $v$ that helps the onward journey and impedes the return journey. If the time taken to go across and return on the rough day is $T$,then $T / T_0$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module