Question

A man who can swim at a speed v relative to the water wants to cross a river of width d flowing with a speed u. The point opposite him across the river is P. a) the minimum time in which we can cross the river is d/v b) he can reach the point p in time d/v c) he can reach the point P in time d/√v²-u² d). He cannot reach P if u>v

Answer 1

Answer:

a) the minimum time in which we can cross the river is d/v  (but not point p)

c)  he can reach the point P in time d/√v²-u²

Explanation:

A man who can swim at a speed v relative to the water wants to cross a river of width d flowing with a speed u. The point opposite him across the river is P

If Man Swims at speed v toward P

then time taken to cross River width d =  d/v

the minimum time in which we can cross the river is d/v

But he would not be able to reach P as River flow will take aside

b) he can not reach the point p in time d/v

To reach P he has to Swim in such a direction that it cancel out river velocity

=> VCosα = -U

& Vsinα is Speed across Width

=> time to reach P = d/VSinα

VSinα = √V²Sin²α  = √V² - V²Cos²α  = √V² - U²

=> he can reach the point P in time d/√v²-u²

if U > V  => Vosα < U  as Cosα < 1

=> He can not cancel River velocity

so he can not reach P  if u>v