Answer to Question #81107 in Classical Mechanics for Laurence

Question

A boat is sailing in the direction of N 16o W at a speed of 225.21 km/h in still air. The wind is blowing to the direction of S 41o W at a speed of 116.69 km/h. Find the principle angle of the resultant.

Answer 1

R_x=v_x+u_x=225.21 cos⁡16+116.69 cos⁡41=304.553 km/h.
R_y=v_y+u_y=225.21 sin⁡16-116.69 sin⁡41=14.479 km/h.
The principle angle of the resultant is
θ=tan^(-1)⁡〖R_y/R_x 〗=tan^(-1)⁡〖(14.479 )/304.553〗=N 2.72° W.