Question

3. A boat goes across a river with a velocity of 8 km/hr, heading directly opposite to the starting point. If the resultant velocity of the boat is 10 km/hr, what is the velocity of the river water? ​

Answer 1

First see the image attached in this given answer it will help you to understand the solution better.

Let the boatman start from point 'A' and pointing towards 'B' which is directly opposite to the starting point.

Although the boatman won't be able to reach the exact opposite point due to the river flow which would obviously cause a drift of certain distance in the direction of river flow.

Velocity of Boat = 8 kmph $j$

where $j$ denotes the direction in Y axis

Velocity of river be = v $i$

$i$ denotest the direction of the velocity of river which is in X axis

since the resultant velocity of the boat is 10 kmph

using traingle law of vector addition and using formula to find the Resultant vector

10 = $10 = \sqrt[]{8^{2} + v^2 + 2(8)(v)cos\alpha }$

where $\alpha$ is the angle between the velocity of boat and velocity of river = 90º

thus

$10 = \sqrt{64+v^2}\\100 = 64 + v^2\\v^2 = 36 \\v = \sqrt{36} = 6 m/s$

Thus the velocity of River is 6 m/s

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