Ghost Ships

[BMAD]

Four ghostly galleons – call them E, F, G and H, – sail on a ghostly sea so foggy that visibility is nearly zero. Each pursues its course steadily, changing neither its speed nor heading. G collides with H amidships; but since they are ghostly galleons they pass through each other with no damage nor change in course. As they part, H’s captain hears G’s say “Damnation! That’s our third collision this night!” A little while later, F runs into H amidships with the same effect (none) and H’s captain hears the same outburst from F’s. What can H’s captain do to avoid a third collision and yet reach his original destination, whatever it may be, and why will doing that succeed?

[DeGe]

The ships are traveling as below:

Now, for H to avoid the collision with I, he needs to stop for a while before restarting the journey.

The time of rest will depend on the time between the 2 collisions and the times at which the other ships started.

Alternatively, he can change course and follow (for a while) the course that F was coming from and then go in the direction of his destination.

[DeGe]

The ships are traveling as below:

Ships.JPG

Now, for H to avoid the collision with I, he needs to stop for a while before restarting the journey.

The time of rest will depend on the time between the 2 collisions and the times at which the other ships started.

Alternatively, he can change course and follow (for a while) the course that F was coming from and then go in the direction of his destination.

I is E above.

[harey]

If I posted this problem, I would ask to clarify:

1) why the lines H and I cannot be parallel;

2) crossing trajectories do not necessarily imply that the ships collide.

BTW, the sea should be endless (so that H does not reach her destination before colliding).

[DeGe]

If I posted this problem, I would ask to clarify:

1) why the lines H and I cannot be parallel;

2) crossing trajectories do not necessarily imply that the ships collide.

BTW, the sea should be endless (so that H does not reach her destination before colliding).

1) Agree. Of course H and I can be parallel. Alternatively, they could even meet/collide at the same point (or just after) the collision between H and F. However, The question is not to find out the exact points at which they collide (if they do).

2) Agree again - that will depend on the relative speeds of the ships. Since no such info is given in the op, the solution must provide for any possible combination of speeds and directions.

The proposed solutions does take that into account.

Edited October 16, 2013 by DeGe