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  • A boat moves with the current from points A to B and returns at the same speed.  The&nb

A boat moves with the current from points A to B and returns at the same speed. 

The speed of the boat relative to the water is η times the speed of the water. The speed of water is 1 m/s.

Find the average speed for the entire trip.

Option: 1

\frac{\eta^2-1}{\eta }


Option: 2

\eta^{2}\ +\ 1


Option: 3

\eta2\


Option: 4

None of the Above.

 


Answers (1)

best_answer

When the boat moves from A to B speed of the boat = \eta+1\

Let t1 be the time taken, then  \eta+1\ =\ \frac{AB}{t_1}\   

Similarly, when the boat moves from point B to A

Speed of the boat = \eta\ -1\

 Let t2 be the time taken,

Then,     \eta-1\ =\ \frac{AB}{t_1}\

Average Velocity =    \frac{2AB}{t_1+t_2}

Substituting the values from above

Average Velocity =   \frac{\eta^2-1}{\eta }


 

Posted by

Devendra Khairwa

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