the same experiments as Figure \[fig:ric\] except we rotated the axes so that $\theta_{cr}(v_{impact})$ is a function of the Froude number or $\bar v_{impact} = v_{impact}/\sqrt{g R_p}$ with $R_p$ the marble radius. The orange dotted line that separates the ricochets from the roll-outs is $$\theta_{cr,ric}^2 = 0.65 - \frac{55}{\bar v^2} 
 \label{eqn:orange}$$ with $\theta_{cr,ric}$ in radians. A similar line, separating roll-outs from stops is shown as a grey dot-dashed line on Figure \[fig:ric\_flip2\]. $$\theta_{cr,roo}^2 = 0.88 - \frac{55}{\bar v^2} .
 \label{eqn:gray}$$

The second term in equation \[eqn:soliman\] is 4 times the square of the Froude number but our orange dotted line requires a number 13 times larger than this. The constant term in Equation \[eqn:soliman\] was predicted to be 1/10th the density ratio. Our substrate to marble density ratio is about 0.64 so the size of the constant term in Equation \[eqn:orange\] is about 10 times higher than expected. The orange dotted line on Figure \[fig:ric\_flip2\] (from equation \[eqn:orange\]) is not consistent with the ricochet model by @soliman76.

The orange dotted line on Figure \[fig:ric\_flip2\] (equation \[eqn:orange\]) represents our first attempt to model the line dividing ricochets from other types of events. This expression will be revisited and improved later on 