Question

A boat is sent across a river with a velocity of 8 km $h^{ - 1} $ . If the resultant velocity of boat is 10 km $ h^{ - 1}$, then velocity of river is

• A. 12.8 km $h^{ - 1} $
• B. 6 km $h^{ - 1} $
• C. 8 km $h^{ - 1} $
• D. 10 km $h^{ - 1} $

Answer 1

The Correct Option is B

To find the velocity of the river, we need to analyze the given data and use vector addition for the velocities involved.

The problem states:

• The velocity of the boat across the river (perpendicular to the river flow) is 8 \, \text{km/h}.
• The resultant velocity of the boat is 10 \, \text{km/h}.

The velocity of the river is what we need to find. Let's denote:

• v_b = 8 \, \text{km/h}
• v_r: velocity of the river
• v_{\text{resultant}} = 10 \, \text{km/h}

These velocities are vectors. The boat's velocity and the river's velocity are perpendicular to each other. The resultant velocity can be found using the Pythagorean theorem:

v_{\text{resultant}}^2 = v_b^2 + v_r^2

Substitute the given values into the equation:

10^2 = 8^2 + v_r^2

Simplifying the equation:

100 = 64 + v_r^2

v_r^2 = 100 - 64 = 36

Taking the square root of both sides yields:

v_r = \sqrt{36} = 6 \, \text{km/h}

Thus, the velocity of the river is 6 km/h.

Let's verify our answer by checking the applicability of the formula:

The given problem correctly follows the concept of vector addition in physics for perpendicular components. Our calculation effectively matches the provided option: 6 km/h.