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Grade: 11
        
Two swimmer's A and B initially on the opposite banks of a river are situated exactly opposite to each other. They can swim with speeds vA = v and vB = v in still water. They start swimming simultaneously at angles A = 30° and B =  with respect to the river. Calculate the time after which they will meet. (given 'd' = width of the river ; v = speed of the river.)
2 years ago

Answers : (2)

Arun
23330 Points
							
Dear Varsha
 
Check if its answer is 
\sqrt3 d /2v
 
If it's correct.then I will tell you the solution.
 
Regards
Arun (askIITians forum expert)
2 years ago
Joe Allan
13 Points
							
Dear Varsha,
Let's take component of velocity of both swimmers along the line joining them(LJT),
So.
Va along LJT =√3v/2
Vb along LJT= vcos\Theta/√3
And from condition for collision we get that relative velocity along river should be zero
Since relative velocity must be only along line joining them,
Va along river =v- v/2=v/2
Vb along river =v(1-sin\Theta/√3)
=>V/2 -v(1-sin\Theta/√3)=0
1/2=sin\Theta/√3
\Theta=π/3
Now coming to line joining them
d=(√3v/2+ v/√3cos\Theta)t
d=(√3v/2+ v/2√3)t
d=(4v/2√3)t
t=√3d/2v
 
 
one year ago
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