## 3 Results  
The inter-relationship between speed measures and total hop distances is presented in Table 1. A near-perfect correlation was observed between the 3-Hop and 5-Hop distances. As the distance increased from 10 m to 40 m, the strength of the correlations between the sprint times and both the 3-Hop and 5-Hop distances also increased, with very high negative and statistically significant (\(p<0.05\)) correlations ranging from r = \(-0.700\) to \(-0.796\). The differences in the 3-Hop and 5-Hop correlations were negligible, ranging from 0.006 to 0.011. The means and standard deviations for the kinetic variables for 3-Hop and 5-Hop are provided in Table 2. In terms of the relationship between 3-Hop and 5-Hop kinetic measures and sprint times (10 and 40 m) the following was observed: the relationships between the kinetic measures and 10 and 40 m sprint times were weak to moderate (\(r<-0.554\)). Among the kinetic measures, relative maximal vertical force exhibited the strongest correlation, particularly across the 3-Hop and 5-Hop sequences (\(r=-0.554\) to \(-0.350\)). Relative net vertical impulse was found to have a weak relationship across steps with sprint times (\(r=-0.360\) to \(-0.270\)), as too was the relative vertical braking impulse across (\(r=-0.339\) to \begin{table}
\begin{tabular}{l l l l l} \hline \hline  & & **10 m** & **20 m** & **40 m** \\ \hline \multirow{2}{*}{3-Hop distance} & Pearson’s \(r\) & \(-0.705\) & \(-0.760\) & \(-0.795\) \\  & \(p\)-value & \(<\)0.001 & \(<\)0.001 & \(<\)0.001 \\ \hline \multirow{2}{*}{5-Hop distance} & Pearson’s \(r\) & \(-0.700\) & \(-0.759\) & \(-0.796\) \\  & \(p\)-value & \(<\)0.001 & \(<\)0.001 & \(<\)0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Inter-relationships between speed measures and 3-Hop and 5-Hop distance. 0.066). Moderate to negligible correlations were found between relative vertical propulsive impulse with sprint times (\(r=-0.404\) to 0.059), with the strongest relationships observed in the initial steps, particularly for shorter sprint distances. Moderate to weak correlations were observed between net relative horizontal impulse and sprint times (\(r=-0.449\) to 0.147), with stronger relationships observed in the first step across all sprint distances. A weak relationship was seen between relative horizontal braking impulse and sprint times (\(r=-0.224\) to 0.259). Moderate to negligible correlations were seen between relative horizontal propulsive impulse and sprint times (\(r=-0.477\) to 0.033), with stronger associations in the initial steps and weaker correlations in the final step. The means and standard deviations for all RSI variables are presented in Table 3. \(\text{RSI}_{\text{hor-DIST}}\) (\(r=-0.453\) to \(-0.707\)) was found to have stronger relationships with sprint performance than \(\text{RSI}_{\text{hor-FT}}\) (\(r=-0.270\) to \(-0.668\)) across all steps and particularly over the initial 5-10 m shorter distances and between fast and slow groups (Table 3). The strength of association of Total \(\text{RSI}_{\text{hor}}\) increased with sprinting distance (0.490 to 0.707; \(p<0.001\)) for both 3-Hop and 5-Hop (Figure 2). The means and standard deviations for the 10 and 40 m fast and slow groups and their differences are shown in Tables 4 and 5. In terms of the 10 m times, faster sprinters were found to produce significantly greater maximal vertical force across all hops (8.55 to 25.6% \(\Delta\)) for both the 3-Hop and 5-Hop testing (ES = 0.784-1.306), significantly greater vertical propulsive impulse (8.41% \(\Delta\)) on the first hop of 5-Hop testing, significantly greater net horizontal impulse on the first hop (20.3% \(\Delta\)) of the 5-Hop test, and significantly greater horizontal propulsive impulse across the first three hops (10.1 to 17.8% \(\Delta\)) in the 5-Hop test (ES = 0.818-1.159).