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THE FLOW SPEED OF WATER VARIES WITH THE DISTANCE FROM ITS STRAIGHT BANK AS V=(1m 1/2 s).z 1/ 2 where z is the perpendicular distance in m from the bank A.SWIMMER ENTERS THE RIVER AT A POINT A ON THE BANK AND SWIMS AT 2m/s, IN A DIRN NORMAL TO RIVER FLOW. WHAT IS HIS DRIFT DOWNSTREAM BY THE TIME HIS NORMAL DISTANCE FROM THE bank IS 20m?

THE FLOW SPEED OF WATER VARIES WITH THE DISTANCE FROM ITS STRAIGHT BANK AS V=(1m1/2s).z1/ 2 where z is the perpendicular distance in m from the bank A.SWIMMER ENTERS THE  RIVER AT A POINT A ON THE BANK AND SWIMS AT 2m/s, IN A DIRN NORMAL TO RIVER FLOW. WHAT IS HIS DRIFT DOWNSTREAM BY THE TIME HIS NORMAL DISTANCE FROM THE bank IS 20m?

Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear vardaan

V=z1/ 2

velocity of man =2 m/sec

time taken by man to swim 20 m in normal direction t= 20/2 =10 sec

 

and time taken be man to swim z distance in normal direction t= z/2............1

 

now consider motion from z to z+dz distance time taken by man to travel z to z+dz postion is dt

and for this small distance dz ,velocity of river assumed to be constant V =z1/ 2

so distance moved in downstreem direction in time dt is

ds =z1/ 2 dt

ds =(2t)1/2 dt  from equation 1

ds =(2t)1/2 dt   

S =√2 t3/2 /3/2  limit o to 10 

   =2√2/3 t3/2    limit o to 10

   =40√5/3

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