# Can cannonballs go through water?

In the recent Spielberg/Jackson Tintin movie, there is a scene where Red Rackham and Captain Haddock's ships are fighting, and cannons are fired. The cannonball is shown at one point to go through a wave, and inflict serious damage on the other ship. I know that bullets stop in water; do cannonballs, with their greater weight, continue with enough force to inflict damage?

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I dont have the time to work out a complete answer, but generally, yes, the momentum of a cannonball would likely be sufficient to both pass through a wave and damage a ship. Of course, it depends on the relative sizes, but, think of it as the wave serving as a shield; the momentum would be reduced, but the ball likely wouldn't stop. –  AdamRedwine Jul 2 '12 at 17:34
It also depends on the length of water the cannonball goes through and on the projectile's shape: bullets are far more aerodynamically shaped than cannonballs. –  Emilio Pisanty Jul 3 '12 at 9:53
However, keep in mind that ship cannons were originally used to break the other ship's masts or damage its hull below the waterline in order to sink it. –  Emilio Pisanty Jul 3 '12 at 9:54

Let's denote the ball's radius by $R$, its speed by $v$, and its mass density by $\rho_{ball}$. The kinetic energy $E_k$ equals $\frac 1 2 M v^2 = \frac{2 \pi}{3} \rho_{ball} R^3 v^2$.
The drag force $F_d$ is given by $\frac 1 2 C_d \rho_{water} v^2 A = \frac {\pi}{2} C_d \rho_{water} v^2 R^2$. Here, $C_d$ denotes the drag coefficient for a sphere.
The maximum distance $L _{max}$ that can be traversed by a cannonball $L_{max} = E_k/F_d$ is therefore $\frac 4 3 \frac {R}{C_d} \frac {\rho_{ball}}{\rho_{water}}$. For typical values ( $\frac{\rho_{ball}}{\rho_{water}} < 8$ and $C_d > 0.1$, see here), we find $L_{max} < 100 R$.