## 1 Introduction
### Ballistics Analysis Approach  
Projectile motion principles are often applied to analyze and predict the trajectory of flyrock fragments propelled by the kinectic energy imparted by explosives with an underlying assumption that the ejected fragment continues its motion on a projectile path unless it experiences an external force. [PERSON] et al. published three serial articles discussing the application of the Ballistics Analysis (BA) approach. The first article [23] proposed a methodology of using ballistic flight equations to predict trajectories of flyrock for post-incident forensic investigations. In this study, the authors analyzed basic forces acting on a flying fragment (Figure 3), highlighting the fragment size and air drag force (\(D\)) as critical influencing factors for the trajectory. Assuming \(\theta\) as 45\({}^{\circ}\) for maximum throw, the flyrock launch velocity was approximated using the established equations of projectile motion. To validate the findings and establish a safe distance for bench blasting operations, flyrock landing positions were visually measured, and damage to nearby equipment and structures was recorded.  
The authors further highlighted the interplay of inertia, launch velocity, mass and cross-sectional area of the fragment, and \(D\) in governing the travel distance of flyrock. It was suggested that additional research is required to refine the equations by integrating a more precise drag coefficient. Subsequently, a second article [24] was published on this topic in which a novel technique of enhancing the accuracy of the determined drag coefficient for flyrock was detailed. The calculation of the drag coefficient involved an analysis of the fragment's movement at terminal velocity. However, it was discovered that the drag coefficient did not produce a unique value, possibly due to the influence of the fragment's  
Figure 3: Basic forces acting on flying fragment [24].  
shape, size, launch velocity, and \(\theta\). In the third article, the authors developed an adaptive system that could predict the launch velocities of flyrock using a 19-8-6-1 architecture Artificial Neural Network (ANN) [25] optimized with a fuzzy algorithm. The predictor demonstrated promising potential in predicting the initial velocity of flyrock fragments. However, it was noted that the predictor was still a concept due to the limited diversity of data resulting from the similar geological conditions at the investigated mining sites. It was further suggested that this limitation could present an opportunity for research aimed at creating a universal prediction model.  
Recently, [PERSON] [26] proposed a probabilistic approach for predicting flyrock range using a detailed BA combined with a mechanistic MCS based on investigational data from six surface mines. The approach involved wind tunnel experiments to determine variable coefficients of drag and lift for each fragment considering the effect of usual winds on the flyrock range. The study presented a two-dimensional (2D) ballistic model that utilized a fourth-order Runge-Kutta scheme to integrate the equations of fragment motion under the variable drag and lift forces. The model predictions were then compared with the probabilities of excessive flyrock range obtained from MCS. Later, the 2D model was extended to a pseudo-three-dimensional (3D) model to examine the impact of prevailing winds and pit-surface topography. At last, a complete 3D model was developed to determine the flyrock range.