Question

16. A boat is sent across a river with a velocity of 8 kmh '. If the resultant velocity of boat is 10 kmh ', then
velocity of the river is
(A) 10 kmh
(B) 8 kmh
(C) 6 kmh
(D) 4 kmh​

Answer 1

$\displaystyle\large\boxed {\sf {|\vec{v_r}|=6\ km\ h^{-1}}}$

The boat is sent with a velocity $\displaystyle\sf {|\vec {v_b}|=8\ km\ h^{-1}}$ perpendicular to the river flow / river bank.

This means the angle between the velocities of the boat and the river is 90°.

The magnitude of the resultant velocity of boat with that of river is,

$\displaystyle\longrightarrow\sf {|\vec {v_b}+\vec {v_r}|=10}$

$\displaystyle\longrightarrow\sf {\sqrt{(v_b)^2+(v_r)^2-2\cdot v_b\cdot v_r\cdot\cos 90^{\circ}}=10}$

$\displaystyle\longrightarrow\sf {8^2+(v_r)^2=10^2}$

$\displaystyle\longrightarrow\sf {(v_r)^2=100-64}$

$\displaystyle\longrightarrow\sf {\underline {\underline {|\vec{v_r}|=6\ km\ h^{-1}}}}$

Answer 2

Answer:

${v}^{2} = 6 {km}^{ - 1}$