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Question

River of width d is flowing with velocity v0 as shown. A swimmer swims (with respect 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 followed by the swimmer is


A
y=x33v30
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B
y=x2v20
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C
y=xv0
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D
y=xv0
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Solution

The correct option is A y=x33v30
For equation of trajectory, we need to find the relationship between Y displacement (y) and X displacement (x).


For swimmer, uy=0,ay=2t
& ux=0,ax=0
Velocity of man w.r.t river,
vmr=aydt=t2^j
Velocity of river
vrg=v0^i with respect to ground.
Velocity of man w.r.t ground, vmg=vmr+vrg
=t2^j+v0^i

Component of velocity of man w.r.t. ground:
vx=v0dxdt=v0
Integrating both sides:
x0dx=v0t0dt
x=v0t ... (i)

Now, vy=t2 dydt=t2
y0dy=t0t2dt
y=t33 ... (ii)

Putting t=xv0 in Eq. (ii),
y=(x33v30)

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