A hostile situation has developed - armed intruders have taken civilians as hostages in a residential home. To rescue the hostages and neutralize the threat, our elite SWAT team must be deployed. However, before they can attempt this extremely high-risk operation, we need to ensure they are properly outfitted with specialized protective gear. The most critical piece of equipment is the helmet each officer will wear. In a scenario where they could face blunt impact forces up to 3000 Newtons, the helmet's shell thickness becomes a crucial factor in preventing severe head injuries. Your task is to analytically determine the minimum required shell thickness to withstand these intense forces, while also incorporating a safety factor of 2 for extra protection. Utilizing your multidisciplinary STEM knowledge, you will derive and calculate the shell thickness value by applying fundamental concepts from algebra, geometry, and physics. This will involve using mathematical formulas, making reasonable assumptions about material properties and helmet dimensions, and ultimately solving for the unknown thickness. Your work must show the step-by-step calculations and reasoning behind the final specification. The lives of the hostages, the SWAT officers, and the success of this ultra-critical rescue mission will depend on your expertise in engineering robust head protection. Time is of the essence - provide your analysis promptly so helmet manufacturing can begin and our team can be deployed into the hostile situation as soon as possible. Stay focused and get this calculation right, officer.