I have done quite a few of these "complex" calculations in the process of working with an accident reconstructionist when I was taking classes as part of my physics major. The area of law enforcement that I eventually get into is accident investigation and there is tons of physics involved. Mainly the basic physics of statics, dynamics and general amoung all the specitally formulas and such.
Some of the things that an investigator needs include the corficient of friction (drag factor) and if it changed (wet vs, dry pavement, dirt, etc). They need to know the impact of your tires on providing additional force back to the road. They need to know when the tires locked and if the car skidded the whole way or more likely the car rolled a few feet than skidded. Measurements from the point of impact including all angles are needed. The coeficient of restitution will generally need to be calculated which is based on a number from calculations besed on how much speed is transfered in the colision. To get the number many formulas are needed and they have ones that include the impact of the cars hitting, crush analysis etc. The mass of the vehicles is also important along with the point of impact. Also determining if the collision was plastic or not plastic (elastic or inelastic) is important.
I reciently did one of these calculations for a street racing accident that came in. It took over 3 sheets of calculations to do. Like mscap said we can usually get the speed to a few MPH. Factors that make the calculations off include driver reaction time, impact angles, slope of the road (incline and side to side), impacts with other objects (curbs, etc) amoung others.
This is very interesting stuff for me. BTW, the honda that was racing was going 92 MPH when colliding with a intrepid. The honda was going 80 MPH right after the collision and 55 MPH when the driver hit the tree... the driver died in the collision. The intrepid skidded into the other lane and stoped after skidding a long way (do not remeber the numbers right now). The coficient of friction was rather high that day as the pavement was hot and the tires were hot.


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