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A swimmer crosses a river with minimum p...

A swimmer crosses a river with minimum possible time 10 Second. And when he reaches the other end starts swimming in the direction towards the point from where he started swimming. Keeping the direction fixed the swimmer crosses the river in 15 sec. The ratio of speed of swimmer with respect to water and the speed of river flow is (Assume contant speed of river & swimmer)

A

`(3)/(2)`

B

`(9)/(4)`

C

`(2)/(sqrt5)`

D

`(sqrt5)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C

`V=`velocity of man w.r.t. river
`u=` velocity of river
`Ararr^2B=(d)/(v)implies10=(d)/(v)impliesd=10`V
`Brarr^tC=(d)/(vcostheta)implies15=(d)/(vcostheta)`
`impliesd=15vcosthetararr`
(i) ^ (ii)`impliescostheta=(2)/(3)impliesectheta=(3)/(2)`
`impliestantheta=(u)/(v)` `sqrt(sec^2theta-1)=(u)/(v)`
`(u)/(v)=sqrt((9)/(4-1))=(sqrt5)/(2)implies(v)/(u)=(2)/(sqrt5)`
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