Grade 11Mechanics

KINEMATICS V2

THE FLOW SPEED OF WATER VARIES WITH THE DISTANCE FROM ITS STRAIGHT BANK AS V=(1m^1/2s).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?

vardaan kumar

16 Years agoGrade 11

1 Answer

Badiuddin askIITians.ismu Expert

16 Years ago

Dear vardaan

V=z^{1/ 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 =z^{1/ 2}

so distance moved in downstreem direction in time dt is

ds =z^{1/ 2}dt

ds =(2t)^1/2 dt from equation 1

∫ds =∫(2t)^1/2 dt

S =√2 t^3/2/3/2 limit o to 10

=2√2/3 t^3/2 limit o to 10

=40√5/3

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