A motorboat is racing towards the north at $25 ext{ km/h}$ and the water current in that region is

Question

A motorboat is racing towards the north at $25	ext{ km/h}$ and the water current in that region is $10	ext{ km/h}$ in the direction of $60^\circ$ east of south. What is the approximate resultant velocity of the boat?

Professor PC Thomas Classes · Answer

Using the Law of Cosines: $R = \sqrt{v_b^2 + v_c^2 + 2v_bv_c\cos(120^\circ)}$. Here $v_b = 25$, $v_c = 10$, and angle $	heta = 180^\circ - 60^\circ = 120^\circ$. $R = \sqrt{625 + 100 + 2(25)(10)(-0.5)} = \sqrt{475} \approx 21.8	ext{ km/h}$, which rounds to $22	ext{ km/h}$.