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)

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 $v_{R}=6 \,km / hr$