The current velocity of a river grows in proportion to the distance from its bank and reaches the maximum value v in the middle. Near the banks the velocity is zero. A boat is moving along the river in such a manner that it is always perpendicular to current and the speed of the boat in still water is u. If the width of river is , the distance through which the boat crossing the river will be carried away by the current is lwo then the value of b is:
Answers
Explanation:
The current velocity of a river grows in proportion to the distance from its bank and reaches the maximum value v in the middle. Near the banks the velocity is zero. A boat is moving along the river in such a manner that it is always perpendicular to current and the speed of the boat in still water is u. If the width of river is , the distance through which the boat crossing the river will be carried away by the current is lwo then the value of b is:
Since we are given that the v
0
is the river velocity at the middle which is maximum and at the banks it is zero.
Given that ∣ v br ∣=vy =dtdy =u .(i)
∣ vr ∣=vx =dtdx =( c2v 0 )y ..(ii)
From Eqs. (i) and (ii) we have,
dx
dy
= 2v 0yucor ∫ 0y ydy=2v 0 uu ∫ 0x
dx or y2 =v 0ucx
At y=2c ,x=4ucv 0
or x
net
=2x=2ucv0
b=1