Two swimmers start from point A on one bank of a river to reach point B on the other bank, lying directly opposite to point A. One of them crosses the river along the straight line AB, while the other swims at right angles to the stream and then walks the distance which he has been carried away by the stream to get to point B. What was the velocity (assumed uniform) of his walking if both the swimmers reached point B simultaneously. Velocity of each swimmer in still water is 2.5 km h − 1 and the stream velocity is 2 km h − 1 .
Text Solution
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3 km/h towards B
Sol. v = velocity of swimmer in still mater = 2.5 km/hr.
u = velocity of stream = 2 km/hr.
For Swimmer 1
Time taken to reach point B
t = 
................ (i)
For Swimmer 2
at v 0 = velocity of walking along shore
Time to reach C
t 1 = 
Time taken in coming from C to B
t 2 = 
= 
∴ Total time
t = t 1 + t 2
= 
+ 
........... (ii)
From (1) and (2)
= 
+ 
⇒ v 0 = 
× u
Putting u = 2 and v = 2.5 km/hr ; v = 2.52.5 km/hr
⇒ v 0 = 3 km/hr.
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