Deep and shallow water waves

[cb625]

Homework Statement

Large ships in general cannot move faster than the phasr speed of surface waves with a wavelength equal to twice the ship's length. This is because most of the propulsive force goes into making big waves under these conditions rather than accelerating the ship.

How fast can a 200m long ship move in very deep water?
As ths ship moves into shallow water, does its maximum speed increase or decrease?

Homework Equations

For deep water waves, water depth h>lambda/4
and v(ph)=square roots of (g/k)

The Attempt at a Solution

The wavelength of surface waves = 2*200m=400m ...
But then I don't know what to do ?

 

[Jhero]

I would like to clarify that the statement about large ships not being able to move faster than the phasr speed of surface waves with a wavelength equal to twice the ship's length is not entirely accurate. While it is true that most of the propulsive force goes into making waves in this scenario, it is not the only factor that determines a ship's maximum speed.

In very deep water, a 200m long ship can theoretically move at a speed of v(ph) = √(g/400m) = 7.07 m/s. However, this is not taking into account the effects of drag and other factors that may limit the ship's speed.

As the ship moves into shallower water, its maximum speed will decrease. This is because the water depth decreases and the wavelength of the surface waves becomes smaller, making it more difficult for the ship to move without creating large waves. Additionally, the drag force on the ship will also increase as it moves into shallower water, further limiting its maximum speed.

To accurately calculate the maximum speed of a ship, we would need to consider all the factors that affect its movement, including drag, wave-making resistance, and the power of the ship's propulsion system. It is not solely determined by the phasr speed of surface waves with a wavelength equal to twice the ship's length.