1. ## fluid dynamics

I have been posed the question

The crests of rollers directly following a ship 67m long overtake it at intervals of 16.5 sec. It takes a crest 6 sec to traverse the length of the ship.
Find the wave length of the rollers and the speed of the ship?

Im stuggling to find where to even start. I know that the wave length is given by (2pi/k) where k is the wave number not sure if this helps

2. ## Partial Soln: Fluid Dynamics

Originally Posted by syster
I have been posed the question

The crests of rollers directly following a ship 67m long overtake it at intervals of 16.5 sec. It takes a crest 6 sec to traverse the length of the ship.
Find the wave length of the rollers and the speed of the ship?

Let the velocity of the ship be v and the velocity of a wave crest be u.

The velocity of the wave relative to the ship is now u - v.

(u - v) * 6 = 67 based on time to traverse the length of the ship.

Now every 16.5 seconds the wave travels one wave length (Y) plus v*16.5 (the distance that the ship has traveled), it also travels 16.5*u, so

v*16.5+Y=u*16.5 , rearranging gives u-v=Y/16.5

Substituting into our earlier equation Y/16.5 * 6 = 67. Solve to get wavelength = 184.25m. And the relative velocity (u-v) is 11.166 m/s.

I don't think the problem can be solved. We can only form two equations and therefore we can only solve for two unknowns (relative velocity and wavelength). Unless this is a trick question? When they say "It takes a crest 6 sec to traverse the length of the ship" do they mean that an observer on the bow will observe the crest 6 seconds after it is observed at the stern, or do they mean it takes 6 seconds to travel 67m? If they mean the second definition then the wave travels at 67/6 m/s and the problem is easy. What's more after 6 seconds the wave crest will not have reached the bow because the ship will have moved.