Crash of two cars: What was the speed of car 1 at imact?

[crash37]

Car 1 hits car 2 and sets car 2 into 180 degree rotation. Both cars are of similar dimensions and about the same weight. What was the speed of car 1 at impact?
Assume that car 2 had a speed of 20 mph (29.3 ft/sec) in the opposite direction at impact.

I am stuck in using the conservation of linear momentum because the rotation of car number 2 involves a rotation of 180 degrees.

The kinetic energy of car 1 is converted into the rotational energy of car 2.
Pi rad = 180 degrees. How do I substitute this into omega squared of 1/2 I omega squared?

 

[crash37]

I assume that car 1 hit car 2 at an angle of 30 degrees from the horizontal.

 

[rcgldr]

You'd have to know the amount of traction there was, then estimate how much energy was lost due to friction and deformation of the car bodies. At the end of the collision the car is no longer rotating, so you don't know how much energy was involved, or the rate of rotation of the car during the time it was rotating.

Conservation of momentum would need to include the change in momentum of the Earth (also a tiny bit to the air), otherwise, if the Earth is ignored, then momentum of the 2 cars is not preserved, since I assume they both end up stopped.

 

[Curl]

you're assuming that all energy stays in the 2-car system, which is false.

Instead of trying to look for formulas to plug and chug, try thinking about it first.

 

[crash37]

Curl,

I agree with you. I don't have any skid marks - car 1 hit me so fast that he was not able to react. I don't know how much energy was absorbed by the deformation of cars 1and 2.

I was hit when I was decelerating in car 2. The end of my fibula where it connects to my ankle bone was shattered. The doc said that this was caused by the impact. Perhaps crash data can answer my question.

I appreciate your comment.