## The Meaning of Special Relativity in a Wave with Medium (3)

With all these solutions, there are some common problems.

Problem 1: The solution will get broken if v ≥ c.

Anyway, the boss will know by his own experience that going upstream is not possible, so the fix is not needed any more.

Problem 2: The solution only works for round trips along the bank.

For one way trip when the direction of c and v are along the same line, the and will not appear.

Problem 3: The solution is direction related.

Our example is only one special case, as Galilean velocity addition is actually vector addition. When the path is in an angle of θ (a value between 0 and 90°) with the bank, the average speed can be calculated this way:

,  where   ,

Let θ=0, we have , this is our case.

Let θ=90°, we have , this is the case when the path is perpendicular to the bank.

Any other angle between 0 and 90° will result in an average speed between these two values. The process leading to this formula is omitted, as it is againt our purpose of make things simpler.

Replace the boss with a water wave with re-bouncing capability, the results will not be affected in any way.