Question

A swimmer wishes to cross a river of width 500 m. River flows at a speed of 4 m/s. Swimmer can swim in still water with 3 m/s. Then
a)Minimum time in which he can cross the river is 166.67 s

b)Drift cannot be zero when he crosses the river in least time

c)Drift can be zero if swimmer chooses an optimum direction

d)The minimum time in which he can cross the river is 125 s​

Answer 1

Given :

Width of the river = 500 m

Velocity of the river (V$_r$) = 4 m/sec

Velocity of the swimmer in still water (V) = 3 m/sec

To Find :

The correct statement among the following

Solution :

Let '∅' be the angle made by the swimmer with the vertical while crossing the river. Component Vcos∅ enables the swimmer to cross the river along AB and the time 't' required for that is -

t =  (Width (L) ÷ Vcos∅)

't' will be minimum when the value of cos∅ is maximum, i.e., cos∅ = 1 or, ∅ = 0°.

Hence, to cross the river in  minimum time, the swimmer should swim along the width of the river.

∴ Minimum time required to cross the river = $\frac{L}{V}$

                                                                        =  $\frac{500}{3}$

                                                                        = 166.67 sec

∴ Minimum time required to cross the river is 166.67 seconds.

Hence option (a) is correct.