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Question

A boat crosses a river with a velocity of 8Kmhr-1. If the resulting velocity of boat is 10Kmhr-1, then the velocity of river water is:


A

4km/hr

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B

6km/hr

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C

8km/hr

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D

10km/hr

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Solution

The correct option is B

6km/hr


Step 1: Given data and drawing the vector diagram of the given situation

Velocity of boat vb=8Kmhr-1

Resultant velocity of boat VB=10kmhr-1

Let velocity of river =V

The vector diagram is given below:

Step 2: Calculating the velocity of river

By observing the vector diagram we can write

Resultantvelocity=(Vb)2+V2+2VbVcos90010=82+V2+2×8×V×010=64+V2

Now squaring on both sides we get

100=64+V2V2=100-64V2=36V=6Kmhr-1

Therefore the velocity of river water is equal to 6kmhr.

Hence, option(B) is the correct answer.


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