A man who can swim at a velocity v relative to water wants to cross a river of width b, flowing with a speed u.

Options

A. (a)The minimum time in which he can cross the river is b/v
B. (b)He can reach a point exactly opposite on the bank in time `t=(d)/sqrt(v^(2)-u^(2))` if `v gtu`
C. (c)He cannot reach the point exactly opposite on the bank if` u gt v`
D. (d)All of the above

Answer

d

Explanation

Time is minimum when he tries to cross the river perpendicular to the current flow `rarr` minimum time = b/v In order to reach the opp. point, he should try to river in such a way that component of its velocity parallel to the river is upstream and equal in magnitude to the river flow. So that net velocity (as seen by a stationery observe on the ground) is perpendicular to river flow
(c ) is alos current becuse if `u lt v` then the count be able to river up to stream