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The current velocity of river grows in proportion to the distance from its bank and reaches the max value v0 in the middle. near the banks velocity is 0. A boat is moving along the river in such manner that the boatman rows his boat always perpendicular to the current. The speed of the boat in still water is u.Find the distance through which the boat crossing the river will be carried away by the current, if the width of the river is d. Also determine the trajectory of the boat.

The current velocity of river grows in proportion to the distance from its bank and reaches the max value v0 in the middle. near the banks velocity is 0. A boat is moving along the river in such manner that the boatman rows his boat always perpendicular to the current. The speed of the boat in still water is u.Find the distance through which the boat crossing the river will be carried away by the current, if the width of the river is d. Also determine the trajectory of the boat.

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
Assume the speed of water and boat(w.r.t to water) be u and v respectively.
width of river = d.
time taken by boat would be,
t = d/v
and
also, v1 = root(u^2 +v^2)
distance covered by the boat,
d = v1 x t =  t*root(u^2 +v^2).
 

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