Final Answer : (a) 200 m

(b) 1/3 m/s

(c) 0.2 m/s

Steps:

1) We are assuming respective velocities are same in both cases and u > v. (see below)

Case 1 : (Crossing in Minimum Time)

=> When man wants to cross the river in minimum time, then he must swim perpendicular to flow of river.

Let the relative velocity of man wrt river be 'v' &

Velocity of river /Speed of current be 'u'.

d - Width of River

2) Time taken to cross the river in minimum time :

Drift = u * t

=> 120 m = u * 600

=> u = 0.2m/s

Therefore,

(c) Speed of current = 0.2m/s

(3) We can also, say :

4) Case - 2 (Crossing with shortest Path) :

Let the relative velocity 'v' make an angle  with vertical in this case .

For Drift to be minimum, (as v < u)

Horizontal component of 'v' must equal to speed of river.

That is,

.

5) Now,

We can say,

6) Now,

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