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Grade 11General Physics

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.)

Varsha

8 Years agoGrade 11

2 Answers

Arun

8 Years ago

Dear Varsha

Check if its answer is

$\sqrt$ 3 d /2v

If it's correct.then I will tell you the solution.

Regards

Arun (askIITians forum expert)

Joe Allan

7 Years ago

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

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