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

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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