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Grade 11General Physics

Using the concept of relative motion answer the question. Velocity of the river with respect to ground is given by v. Width of river is d. A swimmer swims(wrt water) perpendicular to the current with acceleration a=2t where t is time starting from rest from the origin O at t=0.
Find the time of crossing the river.
Find the drift of the swimmer.

Rituraj Singh

12 Years agoGrade 11

2 Answers

Arun Kumar

12 Years ago

Hello Student,

a=2t

v=t^2 since at starting it must be zero

velocity of river=v

since the direction is perpendicular

so there is a drift distance.

dx/dx=t^2

d=t^3/3

=>t=(3d)^(1/3)

=>drift distance =v*(3d)^(1/3)

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

Abc

6 Years ago

a=2t

Since a= dv/dt

Substituting this in the equation

dv/dt = 2t

dv = 2t dt

Integrating both sides

∫dv = ∫2tdt

v = t ²

V is equal to dx/dt

So , substituting this

dx/dt = t²

dx = t ² dt

Integrating both sides we get

x = t³ /3

here x is equal to width of river i.e d

So ,

t = (3d)^1/3

And since the velocity of river is v

The drift will be vt

= v (3d)^1/3

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