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HEDGEHOG- Stop the tank!

Story:

In the heart of a conflict zone, a specialized military unit closely monitored the return of their advanced unmanned tank after a high-stakes reconnaissance mission. As the heavily armoured vehicle approached the unit's forward operating base, the commanders faced a critical challenge. The 50-ton tank, still maintaining its swift pace of 30 km/h, was on a direct collision course with their defensive line.

To halt the tank's momentum and prevent a catastrophic breach, the engineers hastily devised a solid metal hedgehog obstacle crafted from dense steel plates. Failure to precisely calculate the hedgehog's dimensions could result in the unstoppable tank plowing through, jeopardizing the entire operation.

Problem Statement:
A 50-metric ton (50,000 kg) tank is approaching a defensive line at 30 km/h. Engineers must construct a solid metal hedgehog obstacle made of steel with a density of 7,800 kg/m³ to stop the tank's advance. The hedgehog's mass must be equal to or greater than the tank's mass to effectively transfer momentum and bring the tank to a halt.
Challenges:
1. Determine the minimum volume of steel required for the hedgehog to have a mass of at least 50,000 kg.
2. If the hedgehog has a cubic shape, calculate the minimum length of each side to provide the required volume.

To solve this problem, you can introduce the concept of algebraic equations and use variables to represent the unknown dimensions and masses, relating them through density and volume formulas.

Objective
Find the critical size and dimensions of a solid steel cubic hedgehog obstacle large enough to stop the approaching 50-ton tank through its mass and momentum transfer.
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.
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https://arcadebow.notion.site/SWAT-in-Action-Solution-54f43610e3ff48c083cbc6b155d69335

Solution