Question

A motorboat is racing towards the north at 25 $km{h}^{-1}$ and the water current in that region is 10 $km{h}^{-1}$ in the direction of 60${}^{\circ }$ east of south. The resultant velocity of the boat is:

• A. 11 $km{h}^{-1}$
• B. 22 $km{h}^{-1}$
• C. 33 $km{h}^{-1}$
• D. 44 $km{h}^{-1}$

Answer 1

The correct option is B 22 $km{h}^{-1}$

Given,

velocity of the water current $v_c=10km/s$

velocity of the motorboat $v_b=25km/h$

angle between north and south east is ${120}^o$

Resultant velocity $v_R=\sqrt{v_b^2+v_c^2+2v_b{v}_{c}cos{120}^{\circ }}$

$\sqrt{{\left(25\right)}^2+(10{)}^2+2\left(25\right)\left(10\right)\left(\frac{-1}{2}\right)}$ $=22km/h^{-1}$

The resultant velocity of the boat is $22km/h^{-1}$