A swimmer can swim in still water with speed | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the width of the river be $d$.For the shortest time,the swimmer swims perpendicular to the river flow. The time taken is $t = \frac{d}{v}$.For

Vedclass · Accepted Answer

$\sin \,	heta$

Vedclass · Answer

(B) Let the width of the river be $d$.For the shortest time,the swimmer swims perpendicular to the river flow. The time taken is $t = \frac{d}{v}$.For the shortest distance,the swimmer must swim at an angle $	heta$ with the upstream such that the resultant velocity is perpendicular to the river bank. The component of velocity perpendicular to the bank is $v \sin 	heta$ (where $	heta$ is the angle with the upstream). Thus,the time taken is $t' = \frac{d}{v \sin 	heta}$.The ratio of the time taken for the shortest time to the time taken for the shortest distance is $\frac{t}{t'} = \frac{d/v}{d/(v \sin 	heta)} = \sin 	heta$.

Similar Questions

An observer moves with a constant speed along the line joining two stationary objects. He will observe that the two objects

When a train is at rest,rain drops fall vertically. When it moves along east with a velocity equal to that of rain,the rain will appear to fall,for a passenger in the train

$A$ man walking along a straight line with a velocity $6 \text{ km/h}$ encounters rain falling vertically down with a velocity $6\sqrt{3} \text{ km/h}$. At what angle should the man hold his umbrella to protect himself from the rain?

$A$ river is flowing from $W$ to $E$ with a speed of $5 \, m/min$. $A$ man can swim in still water with a velocity of $10 \, m/min$. In which direction should the man swim to take the shortest possible path to reach the opposite bank (South)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module