Q.

Velocity of the river with respect to ground is given by V0 and width of the river is ‘d’. A swimmer swims (with respective to water) perpendicular to the current with acceleration a=2t (where t is time ) starting from rest from the origin ‘O’ at t=0. The equation of trajectory of the path following by the swimmer

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a

y=x33Vo3

b

y=x22Vo3

c

y=x2Vo

d

y=xVo

answer is A.

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Detailed Solution

Displacement along the x-axis is only due to water velocity x=vo×t  ⇒t=xVoAlong the Y− axisa=2t∵a=dVdt⇒dVdt=2t⇒dV=2tdt Integrating on both sides⇒V=2t22  ⇒dydt=t2∵V=dydt⇒dy=t2dt Integrating on both sides⇒y=t33∴y=x33Vo3
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