(B) Let the distance across the lake be $S$.On a calm day,the speed of the boat is $V$. The time taken to go and return is $T_0 = \frac{S}{V} + \frac{

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(B) Let the distance across the lake be $S$.On a calm day,the speed of the boat is $V$. The time taken to go and return is $T_0 = \frac{S}{V} + \frac{S}{V} = \frac{2S}{V}$.On a rough day,the current speed is $v$. The speed during the onward journey is $(V + v)$ and during the return journey is $(V - v)$.The total time taken is $T = \frac{S}{V + v} + \frac{S}{V - v}$.$T = S \left( \frac{V - v + V + v}{V^2 - v^2} \right) = \frac{2SV}{V^2 - v^2}$.Now,calculating the ratio $T / T_0$:$T / T_0 = \frac{2SV / (V^2 - v^2)}{2S / V} = \frac{V^2}{V^2 - v^2}$.Dividing the numerator and denominator by $V^2$,we get $T / T_0 = \frac{1}{1 - v^2 / V^2}$.

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

On a calm day,a boat can go across a lake and return in time $T_0$ at a speed $V$. On a rough day,there is a uniform current at speed $v$ that helps the onward journey and impedes the return journey. If the time taken to go across and return on the rough day is $T$,then $T / T_0$ is:

A
$1 - v^2 / V^2$
B
$\frac{1}{1 - v^2 / V^2}$
C
$1 + v^2 / V^2$
D
$\frac{1}{1 + v^2 / V^2}$

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2 Motion in a Plane

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Relative Velocity (river boat, rain, wind)

$A$ boat crosses a river from one bank $A$ to another bank $B$ which is opposite. The distance between them is $D$. The speed of water is $V_W$ and that of the boat relative to water is $V_B$. If $V_B = 2V_W$, the time taken by the boat to cross the river directly along $AB$ is $(\sin 30^\circ = 1/2, \cos 30^\circ = \sqrt{3}/2)$.

DifficultMHT CET 2026

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$A$ river is flowing from west to east with a speed of $9 \ km \ h^{-1}$. $A$ boat, capable of moving at a maximum speed of $27 \ km \ h^{-1}$ in still water, crosses the river in half a minute. If the boat moves at an angle of $150^{\circ}$ to the direction of the river flow, then the width of the river is:

DifficultJEE MAIN 2025

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$A$ boat crosses a river with a velocity of $8 \, km/h$ relative to the water. If the resultant velocity of the boat with respect to the ground is $10 \, km/h$,then the velocity of the river water is...........$km/h$.

EasyAIPMT 1993

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Particle $A$ moves along the $X$-axis with a uniform velocity of magnitude $10 \ m/s$. Particle $B$ moves with a uniform velocity of $20 \ m/s$ along a direction making an angle of $60^{\circ}$ with the positive direction of the $X$-axis as shown in the figure. The relative velocity of $B$ with respect to $A$ is

MediumWBJEE 2015

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$A$ boy throws a ball in the air at $60^{\circ}$ to the horizontal,along a road with a speed of $10 \, m/s$. Another boy sitting in a passing car observes the ball. Sketch the motion of the ball as observed by the boy in the car,if the car has a speed of $18 \, km/h$. Give an explanation to support your diagram.

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On a calm day,a boat can go across a lake and return in time $T_0$ at a speed $V$. On a rough day,there is a uniform current at speed $v$ that helps the onward journey and impedes the return journey. If the time taken to go across and return on the rough day is $T$,then $T / T_0$ is:

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$A$ boat crosses a river with a velocity of $8 \, km/h$ relative to the water. If the resultant velocity of the boat with respect to the ground is $10 \, km/h$,then the velocity of the river water is...........$km/h$.

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