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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.)
one year ago

Answers : (2)

Arun
19620 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)
one year 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
 
 
5 months ago
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