Two swimmers leeave point A on one bank of the river to reach point B lying right across on the other bank. one of them crosses the river along the straight line AB while the other swims at right angles to the strem and then walks the distance that he has been carried away by the stream to get to point B. what was the velocity U of his walking if both swimmers reached the destination simulteaneously? the stream velociy V =2 km/hr and the velocity W of each swimmer with respect to water =2.5km/hr.

Asked by JAIBHARGAVA200 | 2nd Nov, 2014, 02:17: PM

Expert Answer:

L e t space t h e space f i r s t space s w i m m e r space s t a r t space a t space a n space a n g l e space theta space w i t h space t h e space d i r e c t i o n space p e r p e n d i c u l a r space t o space t h e space r i v e r. T h e n comma space sin theta space equals space v over w T h e space e f f e c t i v e space v e l o c i t y space a l o n g space A B space equals space w space cos space theta space equals space square root of open parentheses w squared minus v squared close parentheses end root T h e r e f o r e comma space t h e space t i m e space t a k e n space b y space f i r s t space s w i m m e r space equals space fraction numerator l over denominator square root of open parentheses w squared minus v squared close parentheses end root end fraction H e r e comma space l space i s space t h e space w i d t h space o f space t h e space r i v e r. T i m e space t a k e n space b y space t h e space s e c o n d space s w i m m e r space equals space l over w T h e space d i s tan c e space b y space w h i c h space h e space d r i f t s space b e y o n d space B space equals space v space cross times space l over w I f space u space i s space t h e space s p e e d space o f space w a l k i n g space o f space t h e space s e c o n d space s w i m m e r comma space t i m e space t a k e n space t o space w a l k b a c k space t o space B space a l o n g space t h e space o t h e r space b a n k space i s space fraction numerator v l over denominator w end fraction divided by u S i n c e space t h e y space r e a c h space s i m u l tan e o u s l y comma space fraction numerator l over denominator square root of open parentheses w squared minus v squared close parentheses end root end fraction equals space l over w plus fraction numerator v l over denominator w u end fraction o r comma space fraction numerator w over denominator square root of open parentheses w squared minus v squared close parentheses end root end fraction equals space 1 plus v over u S o l v i n g comma w e space g e t : u space equals space fraction numerator v over denominator square root of 1 minus begin display style v squared over w squared end style end root minus space 1 end fraction P l u g g i n g space i n space t h e space v a l u e s space a n d space s o l v i n g space f u r t h e r space w e space g e t comma u space equals space 3 space k m divided by h r

Answered by Sheetal Jalan | 2nd Nov, 2014, 04:42: PM