# A motorboat is racing towards the north at 25 kmh-1 and the water current in that region is 10 kmh-1 in the direction of 600 east of south. The resultant velocity of the boat is: (a) 11 kmh-1 (b) 22 kmh-1 (c) 33 kmh-1 (d) 44 kmh-1

Given,

velocity of the water current vc = 10 km/h

velocity of the motorboat vb = 25 km/h

Angle between north and south east = 1800 – 600 = 1200

Resultant velocity of the boat is

$v_{R}&space;=&space;\sqrt{v_{b}^{2}+v_{c}^{2}+2v_{b}v_{c}cos&space;120^{0}}$

$v_{R}&space;=&space;\sqrt{(25^{2}&space;+&space;(10)^{2}&space;+&space;2&space;(25)(10)(-\frac{1}{2})}$

$v_{R}&space;=&space;\sqrt{(625)+(100)-250}$

We get,

vR = 22 km/h-1

Therefore,

The resultant velocity of the boat is 22 km/h-1