r(t) = (^ / 2) ir strength w > 0, and described by the vector w = (-). 4 As the boat progresses, the crew adjusts the sail to orient it parallel to the wind. This generates a constant wind force F = = (F(w)) on the boat, where F(w) > 0 is a function of wind speed only, assumed constant. (a) Find the velocity vector of the boat, v(t), given its trajectory r(t). (b) Calculate the work of the wind force F along the path r(t) for t = [0, 1]. (c) Show that the work of this force is the same along the path F(t) for t = [0, 1], where -((- ((t 1) (t + 1) sinh( + VF). 1+ (t-1) exp( A sailing boat describes a path r(t) = F(t) in the sea, t > 0. The wind is constant, northerly, of t 2+1). (1 + )