*See National Math Standards for this Challenge.*

**Q: How far away will the flyby spacecraft be when the impactor hits Tempel 1?**

This is actually one in a whole series of questions that can only be accurately answered by using some complicated geometry.

It is, however, possible to estimate the answers using simple two-dimensional geometry, so that's what we'll recommend you try.

Looking at the diagram above, you'll see that the impactor and flyby spacecraft separate from each other 24 hours before the impact will occur. The impactor then proceeds into the path of the comet. It should be pointed out that it won't really fly in a straight line as depicted, but will probably follow a slightly more parabolic curve. That's one of the simplifications we'll make in this problem. The impactor will be traveling at a relative speed of 10.2 kilometers per second (km/sec).

The flyby spacecraft heads off at an angle to the path of the impactor. That angle will be approximately 0.033°. The flyby spacecraft will be traveling at a relative speed of 7.6 km/sec at that new heading.

After the impact, the flyby spacecraft continues in its path, taking pictures and spectrometer images until it gets too close to the comet, and has to go into "shield mode" to protect its sensitive instruments from the dust particles in the comet's coma. The minimum safe distance from the comet is 750 km, and the flyby will actually get closer than that.

Okay, you've got all the information you need (believe it or not) to answer the following questions with simple conversions and geometry - they're written in the order that we'd recommend you answer them, but there may be other ways to do this. Try these yourself, and the answers will be presented here later so you can check your work!

- How far will the impactor spacecraft travel between separation and the time of impact?
- What's the closest distance (TCA) the flyby spacecraft will come to the comet?
- How far will the flyby spacecraft travel between separation and the time of impact?
- How far will the flyby spacecraft travel between separation and the point of it's closest approach (TCA)?
- How far will the flyby spacecraft travel between the time of impact and the point of it's closest approach (TCA)?
- How far will the flyby spacecraft travel between the point where it has to enter "shield mode" and the point of its closest approach (TCA)?
- How far will the flyby spacecraft travel between the time of impact and the point where it has to enter "shield mode"?
- How much time will the impactor have to take pictures and images between the time of impact and the point where it has to enter "shield mode"?
- How far away from the comet will the flyby spacecraft be at the time of impact?