(A) To cross a river in the shortest time,the swimmer must maximize their velocity component perpendicular to the river flow.Let the velocity of the m

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(A) To cross a river in the shortest time,the swimmer must maximize their velocity component perpendicular to the river flow.Let the velocity of the man in still water be $v_m = 20\,m/min$ and the velocity of the river be $v_r = 8\,m/min$.The time taken to cross the river of width $d$ is given by $t = \frac{d}{v_m \cos \theta}$,where $\theta$ is the angle with the normal to the river bank.To minimize $t$,the denominator $v_m \cos \theta$ must be maximized.This occurs when $\cos \theta = 1$,which means $\theta = 0^{\circ}$.Therefore,the man should swim perpendicular to the river flow,which is due north.

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

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$A$ river is flowing from west to east at a speed of $8\,m/min$. $A$ man on the south bank of the river,capable of swimming at $20\,m/min$ in still water,wants to swim across the river in the shortest time. He should swim in a direction

A
due north
B
$30^{\circ}$ east of north
C
$30^{\circ}$ west of north
D
$60^{\circ}$ east of north

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3-2.Motion in Plane

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Relative Velocity (river boat, rain, wind)

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DifficultTS EAMCET 2006

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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

DifficultTS EAMCET 2022

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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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The stream of a river is flowing with a speed of $2\,km/h$. $A$ swimmer can swim at a speed of $4\,km/h$. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight (in $^\circ$)?

MediumJEE MAIN 2019

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If a $100 \,m$ long train needs $7.2 \,s$ to cross an object moving in a direction opposite to the train's direction with a speed of $5 \,km/h$, then find the velocity of the train. (in $\,km/h$)

MediumAP EAMCET 2021

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$A$ river is flowing from west to east at a speed of $8\,m/min$. $A$ man on the south bank of the river,capable of swimming at $20\,m/min$ in still water,wants to swim across the river in the shortest time. He should swim in a direction

Similar Questions

$A$ 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:

$A$ 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 $km/hr$.

The stream of a river is flowing with a speed of $2\,km/h$. $A$ swimmer can swim at a speed of $4\,km/h$. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight (in $^\circ$)?

If a $100 \,m$ long train needs $7.2 \,s$ to cross an object moving in a direction opposite to the train's direction with a speed of $5 \,km/h$, then find the velocity of the train. (in $\,km/h$)

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