# find the trajectory of a boat that moves in a river

**1. The problem statement, all variables and given/known data**

A boat part from the point P of the bank of a river, with width D, and that flows with a constant velocity V

_{R}, and moves with a constant velocity V

_{B}, directed towars a point Q, located on the other side of the river directly in front of P. If r is the instantaneous distance of the boat respect to Q and θ is the instantaneous angle between r and PQ, show that the trajectory of the boat is determined by:

r=Dsecθ/(secθ+tanθ)^{VB/VR}

**2. Relevant equations**

**3. The attempt at a solution**

I am completely lost in this problem; I to put the instantaneous distance of the boat r as a vector and a took Q as my origin r = cos(90-θ)i+sen(90-θ)j but then i dont know what else to do; I would appreciate your help a lot

http://ift.tt/1eTIRSj

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