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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?
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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