Applications SAC on Pursuit Curves

[nubs]

Hey guys, we've recently got told that our applications SAC would be related to pursuit curves
It has a bit of a story line, but basically, one guy is running in a straight line with a constant velocity, while 5 others are trying to catch him by following a curved path such that they are always moving directly towards him.
Kind of like what they have here:
http://mathworld.wolfram.com/PursuitCurve.html

Anyway, in this SAC, we're supposed to determine the equation of the pursuit curve (the curved path followed by the 5 other guys)
Also, if the one person will end up escaping from the 5 others or will end up being caught

This is the stuff we need to know:
Calculus – differentiation, integration
Differential equations – exact and approximate solutions
Functions and algebra
Coordinate geometry – gradient, sketch graphs, including asymptotic behaviour
Trigonometry, including the double angle formulas and other identities
Non-accelerated straight line motion
Solving equations – exact and approximate solutions, including use of CAS technology
The use of a CAS calculator to solve differential equations
The use of a CAS calculator to define, differentiate and integrate functions
The use of a CAS calculator to solve equations involving definite integrals

If anyone could give me some advice or tell me how I should go about determining the equation of the curve and if the runner will get caught or not, it would be greatly appreciated
If anyone has any practice material that encompasses all the stuff I listed above, or is similar to that, that would also be great

Thanks

[ninbam1k]

help please, we have a similar sac to this coming up ^.

Cheers.

[nubs]

Well I just finished mine, and if your SAC is anything like mine you'll just be really stressed for time, but otherwise it's not too bad.
Also, pretty much all (linear) pursuit curves can be found like they have done here:
http://online.redwoods.cc.ca.us/instruct/darnold/deproj/sp08/mseverdia/pursuit.pdf
That really helped me^


Only differences are that the straight line might be at a different point or you'll be given values for the respective speeds instead of unknowns

Other than finding the equation of the line, you'll probably just be asked whether or not the escapee will ever be caught, and if so at what coordinates and at what time.

It may look hard at first but it's not that difficult to understand once you read through it a few time
Good luck