183_projects:problem1_spring2021_11 [Projects & Practices in Physics]

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====== Project 11: Part A: Post-Apocalypse Now ======

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Henry Gupta has returned. It turns out he is a pretty bad dude. Gupta hid a remote communication device on the satellite that was activated. It launched many nuclear missiles across the world scorching most of the Earth. 

//100 years later...//

You are a member of the Scorched Earth Army, an elite team of survivors responsible for the protection of and collection of resources for Quadrant 4.

Captain Benjamin L. Willard, Lieutenant Colonel Bill Kilgore, and your team have emerged from your underground bunker to find a deserted wasteland. Well, it's nearly deserted....

Your team is attacked by [[183_notes:supplemental|wild boar-tigers]]. While fighting them off, you manage to slay one of them and collect it for sustenance. Your team returns to the entrance of the bunker only to find it is locked and no one is answering the door.

Your team takes refuge near a fantastic oil fire. It's getting cold and you are hungry. Willard suggests you cook the beast using an age old technique: boiling water in a dirt pit. You'd like to avoid the carcinogens associated with cooking the beast directly over the oil fire. Your team finds a pile of hard and soft rocks near the oil fire. To properly cook the beast, you need to achieve a cooking temperature of 370K. Design the pit.

^                                                 ^ Hard rock ^ Soft rock ^
| Density ($\times 10^{3}\,{\rm kg/m^{3}}$)              |   2.67    |    2.2    |
| Specific Heat Capacity ($\times 10^{3}\,{\rm J/kg/K}$) |   1.0     |    1.4    |

====== Project 11 Solution: Part B: Engineering a movie stunt ======

You and your team have been hired by Marvel Entertainment to develop a stunt for the next offering in the Marvel Cinematic Universe -- Squirrel Girl - New Warrior. This film introduces a new character: Squirrel Girl. 

In a scene meant to take place near the climatic end of the movie, Squirrel Girl (played by Anna Kendrick) is searching for Tippy Toe her squirrel companion on a large hill. While searching, she disturbs a large boulder, which begins to roll down the hill after him. In the scene, Squirrel Girl is meant to sprint down the mountain while the boulder rolls behind him, catching up, but not running over her.

The production studio has designed several boulders (some solid spheres, some hollow spheres, and some cylindrical ones) for the stunt, but doesn't want to manufacture and ship all of them to the set. Also, they have yet to choose a stunt person because they aren't sure how fast that person will need to run down the hill. They've asked your team to design the stunt including the hill and to produce a graph that demonstrates how the speed of the boulder will change as it rolls down the hill. It's foam, but it's big. 

Remember this is Hollywood, so make sure the stunt is exciting!