How Does Relative Motion Affect Navigation Strategy in Maritime Pathfinding?

[j_tang72]

The question is like that.
Q: A ship B is steaming on a straight course south-east at a uniform speed of 15km/h. Another ship A, is a distance of 10 km due north of B and steams at a speed of 12km/h. Find the course that A must steer in order to gets as close to B as possible, and their minimum distance apart.

I want to ask that is that if I find out the relative motion of ship A relative to ship B, will it be helpful to my work? And, if it does, how can I find out the correct course.

Another question is that, does the 10km distance affect the calculation of the relative velocity?

Thx for help

 

[SGT]

Set the two components of the velocity of ship A as functions of the course theta.
Now you can equate the relative velocities in the west-east and north-south axes.
Given the relative velocities, you can equate the components of the distance in the two axes and finally the distance.
If you differentiate the distance in respect to theta and equate it to zero, you find the course that will minimize the distance.
Of course, the initial distance is part of the equation.