(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 2 Motion in a Plane Relative Velocity (river boat, rain, wind)

Medium

$A$ 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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2 Motion in a Plane

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Relative Velocity (river boat, rain, wind)

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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$A$ police jeep is chasing a thief's jeep. The police jeep is moving with a velocity of $45 \, km/h$ and the thief's jeep is moving with a velocity of $153 \, km/h$. The police fire a bullet with a muzzle velocity of $180 \, m/s$. What is the velocity with which the bullet strikes the thief's car in $m/s$?

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The speed of a swimmer is $4\,km\,h^{-1}$ in still water. If the swimmer makes his strokes normal to the flow of a river of width $1\,km$,he reaches a point $750\,m$ downstream on the opposite bank. The speed of the river water is $.........\,km\,h^{-1}$.

MediumJEE MAIN 2023

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The figure shows two ships moving in the $x-y$ plane with velocities $V_A$ and $V_B$. The ships move such that $B$ always remains north of $A$. The ratio $\frac{V_A}{V_B}$ is equal to ........

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$A$ man standing on a road has to hold his umbrella at $30^{\circ}$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \,km/h$. He finds that raindrops are hitting his head vertically. The actual speed of raindrops is:

DifficultTS EAMCET 2006

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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:

The speed of a swimmer is $4\,km\,h^{-1}$ in still water. If the swimmer makes his strokes normal to the flow of a river of width $1\,km$,he reaches a point $750\,m$ downstream on the opposite bank. The speed of the river water is $.........\,km\,h^{-1}$.

The figure shows two ships moving in the $x-y$ plane with velocities $V_A$ and $V_B$. The ships move such that $B$ always remains north of $A$. The ratio $\frac{V_A}{V_B}$ is equal to ........

$A$ man standing on a road has to hold his umbrella at $30^{\circ}$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \,km/h$. He finds that raindrops are hitting his head vertically. The actual speed of raindrops is:

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