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

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