Rain is falling at an angle of 30^{circ} from | vedclass

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

Question

(B) Let the velocity of rain be $\vec{v}_r$. The horizontal component of rain velocity is $v_{rx} = v_r \sin(30^{\circ})$ and the vertical component i

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(B) Let the velocity of rain be $\vec{v}_r$. The horizontal component of rain velocity is $v_{rx} = v_r \sin(30^{\circ})$ and the vertical component is $v_{ry} = v_r \cos(30^{\circ})$.Given that the rain is falling at $30^{\circ}$ from the vertical with a speed of $40 \ m/s$, we have $v_r = 40 \ m/s$.Thus, $v_{rx} = 40 \sin(30^{\circ}) = 40 	imes 0.5 = 20 \ m/s$ and $v_{ry} = 40 \cos(30^{\circ}) = 40 	imes \frac{\sqrt{3}}{2} = 20\sqrt{3} \ m/s$.The car is moving in the opposite direction to the horizontal component of the rain with a speed $v_c = 40 \ m/s$.Let the velocity of the car be $\vec{v}_c = 40 \hat{i} \ m/s$. The velocity of rain relative to the car is $\vec{v}_{rc} = \vec{v}_r - \vec{v}_c$.Assuming the rain's horizontal component is in the negative $x$-direction, $\vec{v}_r = -20 \hat{i} - 20\sqrt{3} \hat{j}$.Then $\vec{v}_{rc} = (-20 \hat{i} - 20\sqrt{3} \hat{j}) - (40 \hat{i}) = -60 \hat{i} - 20\sqrt{3} \hat{j}$.The angle $\alpha$ with the vertical is given by $	an(\alpha) = \frac{|v_{rc,x}|}{|v_{rc,y}|} = \frac{60}{20\sqrt{3}} = \frac{3}{\sqrt{3}} = \sqrt{3}$.Therefore, $\alpha = 	an^{-1}(\sqrt{3}) = 60^{\circ}$.

Rain is falling at an angle of $30^{\circ}$ from the vertical due to the wind with a speed of $40 \ m/s$. $A$ car is travelling horizontally in the direction opposite to the wind, at a speed of $40 \ m/s$. At what angle from the vertical will it experience the rain falling from (in $^{\circ}$)?

Similar Questions

$A$ river is flowing from $W$ to $E$ with a speed of $5 \, m/min$. $A$ man can swim in still water with a velocity of $10 \, m/min$. In which direction should the man swim to take the shortest possible path to reach the opposite bank (South)?

$A$ boat running downstream covers a distance of $16 \, km$ in $2 \, hours$, while for covering the same distance upstream, it takes $4 \, hours$. What is the speed of the boat in still water?

Rain is falling vertically with a speed of $12 \ ms^{-1}$. $A$ woman rides a bicycle with a speed of $12 \ ms^{-1}$ in the east to west direction. What is the direction in which she should hold her umbrella?

Car $A$ is moving to the East with a speed of $30 \text{ km/h}$, and car $B$ is moving to the North with the same speed. What is the velocity of car $B$ as measured from car $A$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module