A boat crosses a river with a velocity of $8 ext{ km/h}$. If the resulting velocity of boat is $10 ext{ km

Question

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

Accepted Answer

1.  **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: $\mathbf{v} = \mathbf{v}_{b} + \mathbf{v}_{r}$ .
2.  **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: $v^2 = v_{b}^2 + v_{r}^2$ .
3.  **Calculation:**
    *   Given: $v_{b} = 8 	ext{ km/h}$ and Resultant $v = 10 	ext{ km/h}$.
    *   Substituting into the formula: $(10)^2 = (8)^2 + v_{r}^2$.
    *   $100 = 64 + v_{r}^2$.
    *   $v_{r}^2 = 100 - 64 = 36$.
    *   $v_{r} = \sqrt{36} = 6 	ext{ km/h}$.

Step-by-Step Solution

Practice All PHYSICS Questions