A motor boat is racing towards North at `25 km//h` and the water current in that region is `10 km//h` in the direction of `60 ^(00` East of South. Find the resultant 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 direction specified by the problem. Using the parallelogram method of addition. Using the parallelogram method of addition, the resultant 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_(c)^(2)+2v_(b)v_(c)cos120^(@)`
`sqrt((25)^(2)+10^(2)+2xx25 xx 10(-1//2)) =~22 km//h`
To obtain the direction, we apply the Law of sines
`R/(sintheta) = v_(c)/(sin theta)` or `sintheta = v_(c)/R sintheta`
`=(10 xx sin120^(2))/(21.8) = (10sqrt(3))/(2 xx 21.8) =~0.397`
`phi =~23.4^(@)`