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

Answer: (B)

6 km $h^{ - 1}$

Answer 2

Let the velocity of river be $v_R$ and velocity of boat is $v_B$
$\therefore$ Resultant velocity = $\sqrt{ v_B^2 + v_R^2 + 2 v_b v_R \, \cos \, \theta}$
(10) = $\sqrt{ v_B^2 + v_R^2 + 2 v_B \, v_r \, \cos \, 90^\circ}$
(10) = $\sqrt{ (8)^2 + v_R^2 }$ or $(10)^2 = (8)^2 + v_R^2$
$v_R^2 = 100 - 64$ or $v_r$ = 6 km / hr