Question

A man can swim with a speed of 4.0 km/h in still water. How long does he take to cross a river 1.0 km wide if the river flows steadily at 3.0 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

Hera, `vecV_m = 4 km h^(-1), vecv_r = 3 km h^(-1)`

OA = 1 km

Let t = time taken by man to reach the other bank

then `t = (OA)/v_m = 1/4 = 0.25 h`

Distance `AB = v_t xx t =3 xx 0.25 = 0.75 km.`

Answer 2

Speed of the man, v_m = 4 km/h

Width of the river = 1 km

Time taken to cross the river = `"Width of river"/"Speed of man"`

`=1/4h = 1/4 xx 60 = 15 min`

Speed of the river, v_r = 3 km/h

Distance covered with flow of the river = v_r × t

`= 3 xx 1/4 = 3/4` km

`=3/4 xx 1000 = 750 m`