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SWAT in Action Module

Story:

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.
Problem Statement:
Bad guys with guns took some people hostage in a house. To save the hostages, the police need to send in their tough SWAT team. But first, the SWAT officers need a special strong helmet that can protect their heads from getting really hurt.
Using math and science, the engineer has to figure out the perfect helmet shell thickness. Getting this calculation exactly right is the most important part of keeping the SWAT team safe when they go in to rescue the hostages from the dangerous bad guys. Challenges:

For the SWAT team's hostage rescue mission, design a helmet that can protect against blunt trauma. The key is calculating the required shell thickness.

Given:

1. Average Head Circumference: 60 cm
2. Expected Impact Force: 3000 N
3. Safety Factor: 2

Use the formula: t = (F * r) / (σ * L)

Where: t = shell thickness (cm) F = 3000 N r = head radius (cm) σ = allowable material stress (MPa) L = helmet length (cm)

Calculate the minimum thickness value using reasonable assumptions for r, σ, and L. Show work step-by-step.

Explain how the calculated thickness provides the necessary protection for officers facing high-impact blunt forces during the operation.

Objective
Calculate the minimum required thickness for the helmet, and what possible material should we use for the helmet?
Bonus question- Can you innovate the helmet design in any other way?
How to Provide a Solution:
1. Understand the Problem.
2. Carefully review the problem statement, story, and any additional information provided.
3. Identify the key constraints, challenges, and objectives.
4. Provide Your Solution with Calculations.
5. Propose a well-reasoned solution that addresses the challenges and constraints.
6. Support your solution with relevant calculations, considering factors related to problems.
7. Utilize the AI assistant to validate your assumptions, calculations, and approach.
Possible Solution Template.
User can submit their solution like this or whichever method they find suitable. Make sure that your solution can be explained to others easily. You can use videos, images, embeddings, programming or anything which you like.
https://arcadebow.notion.site/SWAT-in-Action-Solution-54f43610e3ff48c083cbc6b155d69335

Solution