A river is flowing from east to west at a speed of 5 m / min. A man on south bank of river, capable of swimming 10 m / min in still water, wants to swim across the river in the shortest time. He should swim :-

Question

A river is flowing from east to west at a speed of 5 m / min. A man on south bank of river, capable of swimming 10 m / min in still water, wants to swim across the river in the shortest time. He should swim :- (A) Due north (B) Due north-east (C) Due north-east with double the speed of river (D) None of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/chemistry/4dc5527e4341c178dcb900f9298c1d59-.png" /> y: v cos θ t=d t =( d / V cos θ) t will be minimum, if cos θ is maximum ( cos θ) max =1 ⇒ θ= t To cross the river in minimum time, the man should swim perpendicular to the river flow, i.e. due north.

Q. A river is flowing from east to west at a speed of $5 m / min$ . A man on south bank of river, capable of swimming $10 m / min$ in still water, wants to swim across the river in the shortest time. He should swim :-

Due north

Due north-east

Due north-east with double the speed of river

None of these

$y : v cos θt = d$
$t = \frac{d}{V c o s θ}$
$t$ will be minimum, if $cos θ$ is maximum
$(cos θ)_{m a x} = 1 \Rightarrow θ = t$
To cross the river in minimum time, the man should swim perpendicular to the river flow, i.e. due north.

Q. A river is flowing from east to west at a speed of 5m/min. A man on south bank of river, capable of swimming 10m/min in still water, wants to swim across the river in the shortest time. He should swim :-