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 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. The temperature of the oil fire is 2000K. To properly cook the beast, you need to achieve a cooking temperature of 370K. Design the pit.

Stuck in the wilderness for a number of days and unable to contact the people in your bunker, your team along with Willard and Kilgore set out to find a new safe haven. After traversing the scorched wasteland for a number of days you see postings for “Thunderdome”, which promises “sanctuary for all”. When your team arrives at Thunderdome, you are greeted by the leader of the community Auntie Entity (“Tina” for short) and a 5 story former engineering building with each floor 12 meters high. Your team is told that you all can become members of the community if you can design a defense system based on a bow design that the community has been working on. In addition to vicious boar tigers, zombies have begun to overrun other settlements in the area and Auntie wants to be prepared for their imminent arrival.

They request some specifics for the machine and indicate some constraints:

• It must fire carbon steel harpoons at or below 270 K (it has been found that cooled projectiles have a greater effect on zombies)
• The harpoon can only be fired horizontally but must have the greatest variation in range possible.
• There is an ample supply of 3 kg harpoons.
• Initial tests suggest that to penetrate zombie flesh, harpoons must have a speed of at least 200 m/s.

The engineering building is 60m from a solid, concrete defensive wall of height 30m and thickness 10m surrounding the Thunderdome. Beyond the wall is a 10m horizontal flat ledge followed by a plain that is 10m below ground level to capture the zombie hoards.

You are also supplied with the following materials:

• A spring with a lock mechanism that enables it to be locked at various compressions with a spring constant of (15000 N/m). There is no crank strong enough to compress this stiff spring.
• On each floor of the engineering building is one defender and one concrete block of mass 400kg. The majority of the inhabitants are stationed on the defensive wall.
• You can also request an amount of ice (at $250\,{\rm K}$) but you have to be specific as supplies are low.

Design the defense system including the range/locations outside the defensive wall that your system can reach with the required specifications. Indicate your supply needs to meet the Aunty Entity's requirements in order to keep Thunderdome safe.