How Can You Calculate the Initial Speed in an Inelastic Collision Problem?

[formulajoe]

A car weighing 900 kg is waiting at a stop sign. A car weighing 1200 kg hits the oter car. The cars move .76 m after the collision. The coefficient of friction between the sliding tires and the pavement is .92. I need to find the speed of the car right before the collision.
I don't know what to use. Conservation of momentum doesn't work because I need at least one of the velocities.I can get the work done by friction fairly easily. But i can't get anywhere from there.

 

[Doc Al]

Use conservation of energy (after the collision).

 

[formulajoe]

but using conservation of energy won't work because the final velocity is zero so that sets one side to zero. leaving the other side just 1/2mv^2. I am trying to find the v.

 

[jamesrc]

It's implied that this is a totally inelastic collision (the cars stick together). You can use work-energy to find the velocity of the two cars immediately after the collision:

.5*M*(v')² = μMgd

where M is the total mass (1200+900), v' is the velocity immediately after the collision, μ is the coefficient of friction, and d is the distance the cars slide.

From conservation of momentum, you have mv = Mv', where m is the mass of the first car and v is what you're trying to find.