Challenging Momentum of Collision Problem

[Baslim]

Homework Statement

Two cars A and B slide on an icy road as they attempt to stop at a light. The mass of A is 1100kg, B is 1400kg. The coefficient of kinetic friction between both cars is 0.130. Car A comes to rest at the light, but car B rear-ends car A. After the collision, A comes to rest 8.2m from the collision point, and B 6.1 meters from collision point.
(a) From the distanced traveled by each car, find the speed of each after impact.
(b) Use conservation of momentum to find the speed when B hit A.

Homework Equations

m1v1i + m2v2i = m1v2f + m2v2f

The Attempt at a Solution

I only know how to solve part (b), but I need information from A to actually calculate it. The equation is based on the conservation of momentum. Where the initial velocity of car B is v2i = (m1v1f + m2v2f)/m2 ...I think...

 

[jamesrc]

There is more than one way to solve the first part of a problem. One way, which you may or may not have covered in class yet, is using the work-energy theorem and equating the change in kinetic energy of a car (which is a function of its initial velocity) with the work done by friction (friction force * distance).

Another way to solve the problem (which you should have covered in class) is by using your knowledge of kinematics. You know the initial and final velocity of the car. You also know the friction force on the car (which means you know its acceleration). Combine that with the stopping distance and consider the relationships you covered while studying kinematics - you should be able to write an equation that will allow you to solve the problem.

I hope that helps.