A motorboay is racing towards north at 25 km/h and the water current in that region is 10km/h in the direction of 60^(@)east ofsouth . Findthe resultant velocity of the boat.

A motorboay is racing towards north at 25 km/h and the water current i

1.	A motorboay is racing towards north at 25 km/h and the water current in that region is 10km/h in the direction of 60^(@)east ofsouth . Findthe resultant velocity of the boat.
Answer» SOLUTION :The VECTOR `v_(b)` representing the velocity of the motorboat and the vector `v_(e)` representing the water current are shown in Fig . 4.11 in direstions specifiedby the problem . Usingthe parallelogram METHOD of addition , the resultantR isobtained 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)+2xx25xx10(-1//2))~=22km//h` To obtain the direction , we apply the Law of SINES `(R)/(sintheta)=(v_(c))/(sinphi)or,sinphi=(v_(c))/(R)sintheta` `=(10xxsin120^(@))/(21.8)=(10sqrt(3))/(2xx21.8)~=0.397` `phi~=23.4^(@)`