A motorboat is racing towards north at 25km/h and the water current in that region is 10 km/h in the direction of `60^(@)` east of south. Find the resulant velocity of the boat.

Explanation

The vector `v_(b)` representing the velocity of the motorboat and the vector `v_(c)` representing the water current are shown in Fig. in directions specified by the problem. Using the parallelogram method of addition, the resulatant R is obtained in the direction shown in the figure.

We can obtain the magnitude of R using the Law of cosine :
`R = sqrt(v_(b)^(2) + v_(e)^(2) + 2v_(b)v_(c) cos 120^(@))`
`= sqrt(25^(2) + 10^(2) + 2 xx 25 xx 10(-1//2)) ~= 22` km/h
To obtain the direction we apply the law of sines
`(R)/(sin theta) = (v_(c))/(sin phi)` or `sin phi = (v_(c))/(R) sin theta`
`= (1 xx sin 120^(@))/(21.8) = (10sqrt(3))/(2 xx 21.8) ~= 0.397`
`phi ~= 23.4^(@)`.