Question

A boat is sent across a river with a velocity of $8km{h}^{-1}$ . If the resultant velocity of boat is $10km{h}^{-1}$, then velocity of river is

• A. $12.8km{h}^{-1}$
• B. $6km{h}^{-1}$
• C. $8km{h}^{-1}$
• D. $10km{h}^{-1}$

Answer 1

Answer: (B)

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