Find the trajectory of a boat that moves in a river

[david22]

Homework Statement

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)^V_B/V_R

Homework Equations

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 don't know what else to do; I would appreciate your help a lot

 

[ehild]

Homework Statement

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)^V_B/V_R

Homework Equations

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 don't know what else to do; I would appreciate your help a lot

Have you copied the problem text correctly? "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 the boat moves with constant velocity it never reaches point Q. Was not it constant speed with respect to the river?

You are right, treat the position and velocity of the boat as vectors. The velocity of the boat with respect to the river points towards Q. What is the velocity of the boat with respect to the shore?

ehild