# Is there any formula to calculate the impact when falling onto water surface from speed?

So I know how to do the math of instantaneous speed when doing free fall:

$$v = g \cdot t$$

and here comes into my question: how can I calculate the impact on water surface when hitting it at a certain speed? For example:

• How much impact would I receive when hitting the water with speed 10m/s?
• How much impact would I get when hitting the water after 3s? (Initial speed is 0)

... And that's it; I don't know if it's possible to do, but just curious.

In order to get a rough estimate, let's make the following approximation: when the falling object is fully submerged its velocity is $$0$$. This is close to the truth for someone hitting the water at fast velocities not in a diving position. Let's also assume that a human being is a cube with mass $$m$$ and side length $$L$$.
When the bottom of the cube is just barely touching the water, i.e. its center of mass's height above the water is $$L/2$$, the cube is travelling at its free fall velocity $$v$$. When the cube is fully submerged, i.e. its center of mass height above the water is $$-L/2$$, and the cube has a velocity of $$0$$. Therefore, after travelling a distance of $$L$$, its velocity has reduced from $$v$$ to $$0$$. From the equation
\begin{align} v_f^2 - v_i^2 &= 2 a \Delta y \\ - v^2 &= -2 a L \end{align} where here we assume the cube undergoes constant acceleration, we see that $$F = ma = m \frac{v^2}{2L}.$$