Question

given that speed of boat in still water is u and velocity of river is v , then calculate the time taken by boat to reach a place downstream at a distance d and back to original position? 1)2vd/v²-u² 2)2ud/u²-v² 3)vd/v²-u² 4)ud/u²-v²​

Answer 1

Answer:

given that speed of boat in still water is u and velocity of river is v , then calculate the time taken by boat to reach a place downstream at a distance d and back to original position? 1)2vd/v²-u² 2)2ud/u²-v² 3)vd/v²-u² 4)ud/u

Answer 2

2)$\frac{2du}{ u^{2} - v^{2} }$ is the solution.

Explanation,

Given,

• The speed of a boat in still water is u m/s.

• The speed of the river is v m/s.

To find,

The time taken by boat to reach a place downstream at a distance d and back to the original position.

Solution,

When the boat will travel downstream, the velocity of the river will contribute to its total velocity and help the boat reach the point at a distance d faster.

Total velocity when the boat travels downstream = (u + v)m/s

Time taken = distance/ speed

$t_{1} = \frac{d}{u + v}$

When the boat will travel upstream, the velocity of the river will act in the opposite direction and pose difficulty for the boat to reach its starting point.

Total velocity when the boat travels downstream = (u - v)m/s

Time taken = distance/ speed

$t_{2} = \frac{d}{u - v}$

Total time taken, $t_{1} + t_{2}$

$t_{1} + t_{2}$ = $\frac{d}{v +u} + \frac{d}{u - v}$

          $= \frac{2du}{ u^{2} - v^{2} }$

Therefore, the total time taken would be $\frac{2du}{ u^{2} - v^{2} }$.