Question

A man can swim with a speed of 4 km h in still water how long does he take to cross a river 1 km wide if the river flows steadily at 3 km h and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?

Answer 1

Answer: 15 min 2nd 0.75km

Explanation: man speed = 4 km/h (across the river)

river width = 1 km

river velocity =  3 km/h (along the river)

(as the velocity of others doesn't affect another velocity when they are perpendicular ) ( its a law )

$time \: taken\: by = \frac{width \:of \:the \:river}{velocity \:of \:man} \\= \frac{1 km}{40 km/hr} (as \: 1hr= 60\:min) \\=\frac{60 min}{4} \\=\frac{15min}{1} \\= 15 min\\ he \:take \:15\:min \:to \:cross \:a \:river\: 1 \:km \:wide$

now we have to find the distance he travel along the river

$distance \: travelled = velocity \:of \:river \:\times \:time \:taken \:to \:reach \:other \:side\\= 3km/hr \times 15min\\=\frac{3 \times 15}{60}(as\: unit \:correction) \\=0.75km$

he is 0.75 km far when he reaches the other bank.

i hope this solution helps