IIT JEE , AIEEE Forum - Physics , Mechanics - motion in 1-d

rshm15varma

The current velocity of the river grows in proportion to the distance from its bank and reaches the maximum value v₀ in the middle.Near the banks velocity is 0.A boat is moving along the river such that its always perpendicular to the current.THe speed of the boat in still water is u.Find the distance thru wich the boat crossing the river will be carried away by the current if the width of the velocity is c.also determine the trajectory of the boat.

joyfrancis

width of velocity??what's that?

rshm15varma

sorry,thats width of river

phyana

i think we require small scale integration.
let the velocity of the currenet at a ditance x from bank1 = constant * x

at x=c/2
v0 = constant *c/2
ie constant=2v0/c

that relation for current velocity upto middle =2v0/c * x

now consider a distance x from the other bank2.
current velocity = (2v0/c)*x

from bank1 distance to this point be L
the x=c-L
sub in the eq
u get.........
velocity = (2v0/c)(c-L)

= 2v0 -( 2vo/c)l
ie after the middle the velocity varies linearly.

time taken by the boat=c/u
horizontal dis from bank1= (intrgral)c/2u * 2vo/c*x*dx
in the limits o to c/2
further integerate c/2u *( 2v0 -( 2vo/c)L )*dL
in the limits c/2 to c

sum up
this is the total displacement

rate me plz if u plz

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