(D) The total distance to be covered is $2d$ (distance $d$ upstream and $d$ downstream).In still water, the man swims at speed $2v$. The time taken to

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(D) The total distance to be covered is $2d$ (distance $d$ upstream and $d$ downstream).In still water, the man swims at speed $2v$. The time taken to cover distance $2d$ is $t_0 = \frac{2d}{2v} = \frac{d}{v}$.When swimming downstream, the effective speed is $v_{down} = v_m + v_r = 2v + v = 3v$. The time taken is $t_1 = \frac{d}{3v}$.When swimming upstream, the effective speed is $v_{up} = v_m - v_r = 2v - v = v$. The time taken is $t_2 = \frac{d}{v}$.The total time taken is $t = t_1 + t_2 = \frac{d}{3v} + \frac{d}{v} = \frac{d + 3d}{3v} = \frac{4d}{3v}$.Therefore, the ratio is $\frac{t}{t_0} = \frac{4d/3v}{d/v} = \frac{4}{3}$.

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

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$A$ 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

TS EAMCET 2022 All TS EAMCET

A
$\frac{1}{2}$
B
$\frac{3}{2}$
C
$\frac{3}{4}$
D
$\frac{4}{3}$

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2 Motion in a Plane

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Relative Velocity (river boat, rain, wind)

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Consider two observers observing a single moving object,and one observer observing two moving objects. Explain the concept of relative velocity in these scenarios.

Medium

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$A$ swimmer can swim with a velocity of $12 \, km/h$ in still water. The water flowing in a river has a velocity of $6 \, km/h$. The angle with respect to the direction of flow of the river water at which the swimmer should swim in order to reach the point on the other bank just opposite to his starting point is ........$^{\circ}$. (Round off to the Nearest Integer)

DifficultJEE MAIN 2021

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$A$ swimmer wants to cross a river which is flowing at a speed $v$. If the swimmer can swim in still water at speed $V$,the direction he should swim to cross the river in the least time is

EasyAP EAMCET 2023

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Match Column-$I$ with Column-$II$ correctly.

Column-$I$ Column-$II$

$(1)$ Velocity of $A$ relative to $B$ if $A$ and $B$ are moving perpendicular to each other $(a)$ $\vec{v}_{rm} = \vec{v}_r + \vec{v}_m$

$(2)$ Velocity of rain drops relative to a man $(b)$ $\vec{v}_{AB} = \vec{v}_A + \vec{v}_B$

$(c)$ $v_{AB} = \sqrt{v_A^2 + v_B^2}$

Column-$I$	Column-$II$
$(1)$ Velocity of $A$ relative to $B$ if $A$ and $B$ are moving perpendicular to each other	$(a)$ $\vec{v}_{rm} = \vec{v}_r + \vec{v}_m$
$(2)$ Velocity of rain drops relative to a man	$(b)$ $\vec{v}_{AB} = \vec{v}_A + \vec{v}_B$
	$(c)$ $v_{AB} = \sqrt{v_A^2 + v_B^2}$

Easy

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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

DifficultAP EAMCET 2019

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Consider two observers observing a single moving object,and one observer observing two moving objects. Explain the concept of relative velocity in these scenarios.

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