Question

A boat crosses a river of width 1 km, which is flowing with a speed of 4 km/h, in minimum time. If the speed of boat in still water is 5 km/h, then drift of the boat when it will reach to other bank is
(1) 800 m
(2) 400 m
(3) 600 m
(4) 200 m
​

Answer 1

Given that,

Width of river = 1 km

Speed of boat = 4 km/h

Speed of water = 5 km/h

We need to calculate the time

Using formula of speed

$v =\dfrac{d}{t}$

$t=\dfrac{d}{v}$

Where, t = time

d = distance

v = speed of water

Put the value into the formula

$t=\dfrac{1}{5}$

$t=0.2\ h$

We need to calculate the distance

Using formula of speed

$\dfrac{d}{t}=\sqrt{v^2-u^2}$

$d=t\times\sqrt{v^2-u^2}$

Put the value into the formula

$d=0.2\times\sqrt{5^2-4^2}$

$d=0.6\ km$

$d=600\ m$

Hence, The distance is 600 m.

(3) is correct option.