While traveling on a highway, a Jaguar behind me (avg. weight 3,400 lbs) skidded on some ice, hit the center divider, bounced off, continued approximately 50 ft on a 20 degree upward incline and struck me. She conveniently doesn't remember how fast she was going. Is there any formula to figure out her speed. I was travelling 35 mph (which I thought was fast given the icy condition of the road), so I know she was going faster than that. I would greatly appreciate any help.

The state police should figure this out and put it in their accident report. You might want to check the accident report and see what the trooper estimated her speed at. If he properly investigated the accident and saw the tire skid marks on the highway (or lack of skid marks) he is probably going to be pretty close to what her actual speed was at the time of the accident. Also take into account the ice thickness - if you remember it.

The officers did not "properly investigate the accident". They got her information and asked her some questions but did not mention anything else. The report is one page. I meanwhile had been knocked unconscience with a concussion and was being taken to the hospital. So basically, I don't know what happened and she conveniently doesn't remember what happened. Her insurance company is blaming it ALL on the ice and doesn't want to pay.

With the ice it is not possible normally to get a exact speed.

Also if the officer used a standard traffic investigation form, they are several pages long and would include a drawing of what happened. Weather conditions and statements of each driver is available and names of witness.

Also remember most police officers are not trained in accident investigation, very few are trained on the determining the speed of a car.
They have basic training in filling out a accident report.
There are several advanced classes in accident reporting, that take several days but most departments have limited budgets to pay for all the classes, they have radar clases that have to be done every two years, they have weapons classes, they have criminal investigation, and 100's of classes. Often a officer has to chose one class per year to go to.

How about a formula for the basics. How much velocity does a 3,400 lb. object need to travel 50ft. Up a 20 degree incline? Does anyone know how to figure this out?

Assuming that the object is coasting up the ramp (no friction, and no extra push from the object's engine) - you calculate this from:



Which for a 50-foot long 20 degree incline turns out to be:


So with an initial velocity of 22.6 MPH the object would coast up the ramp and come to a stop after 50 ft. I must say that a 20 degree ramp is awfully steep for a car - was this a driveway on a hill? Most public roads are no more than about 10 degrees max.

Really? A car only needs to be going about 23mph to slide 50ft UP a hill? It was on a highway going up an overpass. In the formula, what does g stand for? And h?

This formula assumes no friction between the car and the road - in other words, the driver does not apply the brakes at all, and the car doesn't hit anything. Obviously this doesn't correspond to the real world where case of a car "sliding" up a hill, unless it was on super slick black ice with absolutely zero traction. If the driver applied the brakes fifty feet before impact then 22.6 MPH is the lower bound of the true initial speed. Also, if the car impacted anything (like, say, your car) then 22.6 MPH is the lower bound of the change in velocity between the time the car hit yours and its initial velocity. So if you knew that the car hit yours at, say, 20 MPH, then you know that the other car's initial velocity was at least 20 MPH + 22 MPH = 42 MPH.

In the formula g = acceleration due to gravity (which is 32.2. ft/s^2) and h is the height the object moves upward against gravity - here that would be 50 ft times sine(20 degrees).

It is the ice thing, I have seen cars slide 50 ft going 30 miles a hour on ice easy
Then you have to remember it is not from the point where the car ended up at, since cars will still move after their point of initial impact, so you have to also determine the point where the cars hit, and where they moved after initial point of impact.

I believe the other driver hit a patch of ice, not that the whole highway was covered with ice. I'm guessing she hit me on the incline somewhere, since I ended up at the top of the overpass. I live in Texas, ice is a mystery too most drivers here. The day I got hit was the one day that year that the weather was that bad.