(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 3-2.Motion in 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

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

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3-2.Motion in Plane

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Relative Velocity (river boat, rain, wind)

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