When a car is at rest,its driver sees rain dr | vedclass

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

Question

(D) Let the velocity of rain be $\vec{v}_r = -v_r \hat{j}$ and the velocity of the car be $\vec{v}_m = v_m \hat{i}$.When the car moves with speed $v$,

Vedclass · Accepted Answer

$0.73$

Vedclass · Answer

(D) Let the velocity of rain be $\vec{v}_r = -v_r \hat{j}$ and the velocity of the car be $\vec{v}_m = v_m \hat{i}$.When the car moves with speed $v$,the relative velocity of rain with respect to the car is $\vec{v}_{r/m} = \vec{v}_r - \vec{v}_m = -v_r \hat{j} - v \hat{i}$.The angle $	heta$ with the horizontal is given by $	an 	heta = \frac{|v_r|}{|v_m|}$.Given $	heta = 60^{\circ}$ and $v_m = v$,we have $	an 60^{\circ} = \frac{v_r}{v} = \sqrt{3}$,so $v_r = v\sqrt{3}$.When the car speed increases to $(1+\beta)v$,the new angle is $45^{\circ}$.Thus,$	an 45^{\circ} = \frac{v_r}{(1+\beta)v} = 1$.Substituting $v_r = v\sqrt{3}$,we get $\frac{v\sqrt{3}}{(1+\beta)v} = 1$.$\sqrt{3} = 1 + \beta$.$\beta = \sqrt{3} - 1 \approx 1.732 - 1 = 0.732$.Therefore,the value of $\beta$ is close to $0.73$.

Similar Questions

Two parallel rail tracks run north-south. Train $A$ moves north with a speed of $54 \; km \; h^{-1},$ and train $B$ moves south with a speed of $90 \; km \; h^{-1}.$ What is the velocity of the ground in $m \; s^{-1}$ with respect to train $B$?

$A$ ship $A$ is moving Westwards with a speed of $10 \, km \, h^{-1}$ and a ship $B$,$100 \, km$ South of $A$,is moving Northwards with a speed of $10 \, km \, h^{-1}$. The time after which the distance between them becomes shortest is ........ $hr$.

$A$ swimmer crosses a river of width $d$ flowing at velocity $v$. While swimming,he heads himself always at an angle of $120^{\circ}$ with the river flow and on reaching the other end he finds a drift of $d/2$ in the direction of flow of river. The speed of the swimmer with respect to the river is

$A$ 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?

Vedclass Test Series

Exam Paper Generator

Online Exam Module