Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

A boat crosses a river with a velocity of $8 \text{ km/h}$ . If the resulting velocity of boat is $10 \text{ km/h}$ , then the velocity of river water is:

4 km/h

6 km/h

8 km/h

10 km/h

Step-by-Step Solution

Vector Addition: The motion of the boat crossing the river involves two velocity vectors: the velocity of the boat with respect to the water ( $\mathbf{v}_{b}$ ) and the velocity of the river water with respect to the ground ( $\mathbf{v}_{r}$ ). The resulting velocity of the boat with respect to the ground ( $\mathbf{v}$ ) is the vector sum: $\mathbf{v} = \mathbf{v}_{b} + \mathbf{v}_{r}$ .
Right-Angled Triangle: When a boat crosses a river (typically heading perpendicular to the flow to cross), the velocity vectors $\mathbf{v}_{b}$ and $\mathbf{v}_{r}$ are perpendicular to each other. The magnitude of the resultant velocity is given by the Pythagorean theorem: $v^2 = v_{b}^2 + v_{r}^2$ .
Calculation: Given: $v_{b} = 8 \text{ km/h}$ and Resultant $v = 10 \text{ km/h}$ . Substituting into the formula: $(10)^2 = (8)^2 + v_{r}^2$ . $100 = 64 + v_{r}^2$ . $v_{r}^2 = 100 - 64 = 36$ .

$v_{r} = \sqrt{36} = 6 \text{ km/h}$ .

Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started