You need to recover HAL. HAL, if you remember, was a part of the satellite ($m_{\rm t}=4500\,{\rm kg}$) that the Carver Media Group Network (CMGN) launched. The satellite (and HAL) was designed to communicate with Earth out to a distance of 3.8 million kilometers. As part of the electronics HAL contains a green and a red light-emitting diode (LED) mounted on the outer surface of the satellite. One of the probes ($m_{\rm p}=400\,{\rm kg}$) remains attached to a single, very stiff spring ($k_{\rm p}=5.3\times10^{9}{\rm N/m}$) that can be compressed remotely and then released to fire off the probe. You have hacked into this remote firing mechanism.

Unfortunately, a transcription error was made by Mr. Stamper, Carver's chief “engineer” when the satellite was initially launched. As a result, the satellite escaped Earth's gravity and is currently traveling in a straight line away from the Earth at a distance of 1.9 million kilometers. Its speed is nearly constant at $340\,{\rm m/s}$. The gyroscope system that keeps the orientation of the satellite constant is still working. However, an asteroid ($m_{\rm a}=9300\,{\rm kg}$) traveling at a speed of $950\,{\rm m/s}$ is on a direct collision course (in line with the Earth and HAL) and the collision is imminent. The asteroid is presently 500 kilometers from the satellite.

Your team can recapture the satellite if it can be returned to Earth. You should design a way to return the satellite to Earth. You will also need to ensure the asteroid will not collide with the satellite - damaging the probe is ok. Your team also needs to determine the minimum amount of time until the possible collision to determine if a communication from Earth can be completed in time.

• Energy Conservation
• Thermal Energy
• Specific Heat Capacity
• Thermal Equilibrium

</WRAP>

As the satellite, you attempted to save came back into the Earth's atmosphere a remote communication device on the satellite was activated and 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.