(A) First,convert the speed of the car from $km/h$ to $m/s$:$v_m = 40 \times \frac{5}{18} = \frac{200}{18} = \frac{100}{9} \, m/s$.The velocity of the

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$\tan^{-1} \left(\frac{5}{9}\right)$

(A) First,convert the speed of the car from $km/h$ to $m/s$:$v_m = 40 \times \frac{5}{18} = \frac{200}{18} = \frac{100}{9} \, m/s$.The velocity of the rain is $v_r = 20 \, m/s$ (vertically downwards).The relative velocity of the rain with respect to the car is the vector sum of the velocity of the rain and the negative velocity of the car.The angle $\theta$ with the vertical at which the rain strikes the windshield is given by:$\tan \theta = \frac{v_m}{v_r}$Substituting the values:$\tan \theta = \frac{100/9}{20} = \frac{100}{9 \times 20} = \frac{5}{9}$.Therefore,$\theta = \tan^{-1} \left(\frac{5}{9}\right)$.

Class 11 Physics 3-2.Motion in Plane Relative Velocity (river boat, rain, wind)

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$A$ car with a vertical windshield moves in a rainstorm at a speed of $40 \, km/h$. The raindrops fall vertically with a constant speed of $20 \, m/s$. The angle at which the raindrops strike the windshield is .........

A
$\tan^{-1} \left(\frac{5}{9}\right)$
B
$\tan^{-1} \left(\frac{9}{5}\right)$
C
$\tan^{-1} \left(\frac{3}{2}\right)$
D
$\tan^{-1} \left(\frac{2}{3}\right)$

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3-2.Motion in Plane

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Relative Velocity (river boat, rain, wind)

$A$ river has a steady speed of $v$. $A$ man swims upstream for a distance of $d$ and swims back to the starting point in a total time $t$. The man can swim at a speed of $2v$ in still water. If the time taken by the man in still water is $t_0$ to complete the same total distance of $2d$, then $\frac{t}{t_0}$ is

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Two trains $A$ and $B$ travel on two parallel rail tracks in opposite directions with speeds $v_1$ and $v_2$, respectively. They take $4 \ s$ to pass each other at these speeds. If the speed of train $A$ is increased by $50 \%$, then they take $3 \ s$ to pass each other. The ratio $v_1 / v_2$ is:

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Two cars $A$ and $B$ are moving with the same speed of $45\,km/h$ along the same direction. If a third car $C$ coming from the opposite direction with a speed of $36\,km/h$ meets the two cars in an interval of $5\,min$,the distance of separation between the two cars $A$ and $B$ should be.......$km$.

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Ship $A$ is moving westwards with a speed of $20 \ km h^{-1}$ and another ship $B$ which is at $200 \ km$ south of $A$ is moving northwards with a speed of $10 \ km h^{-1}$. The time after which the distance between them is shortest and the shortest distance between them are respectively

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$A$ boat having a speed of $5 \, km/hr$ in still water crosses a river of width $1 \, km$ along the shortest possible path in $15 \, minutes$. Find the speed of the river in $km/hr$.

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$A$ car with a vertical windshield moves in a rainstorm at a speed of $40 \, km/h$. The raindrops fall vertically with a constant speed of $20 \, m/s$. The angle at which the raindrops strike the windshield is .........

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Two trains $A$ and $B$ travel on two parallel rail tracks in opposite directions with speeds $v_1$ and $v_2$, respectively. They take $4 \ s$ to pass each other at these speeds. If the speed of train $A$ is increased by $50 \%$, then they take $3 \ s$ to pass each other. The ratio $v_1 / v_2$ is:

Ship $A$ is moving westwards with a speed of $20 \ km h^{-1}$ and another ship $B$ which is at $200 \ km$ south of $A$ is moving northwards with a speed of $10 \ km h^{-1}$. The time after which the distance between them is shortest and the shortest distance between them are respectively

$A$ boat having a speed of $5 \, km/hr$ in still water crosses a river of width $1 \, km$ along the shortest possible path in $15 \, minutes$. Find the speed of the river in $km/hr$.

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