Determining position of an object after inelastic collision

[Synchron]

Homework Statement

A 39,000 lb truck A and a 3968 lb sports car B collide at an intersection. At the moment of the collision, the truck and the sports car are traveling with speeds vA = 70 mph and vB = 30 mph. Assume that the entire intersection forms a horizontal surface. Letting the line of impact be parallel to the ground and to the pre-impact velocity of the truck, determine the post impact velocities of A and B if A and B become entangled. Furthermore, assuming that the truck and the car slide after impact and that the coefficient of kinetic friction is 0.9, determine the position at which A and B come to a stop relative to the position they occupied at the instant of impact.

Homework Equations

What is required for the problem are the conservation of momentum and energy equations

The Attempt at a Solution

I've already determined the post impact velocities of A and B if they're entangled. The initial i component is the mass of car x vBand the final i component is the combined mass of car and truck x vi( i component of post impact velocity). Same is said for j component with initial as mass of truck x vA and the final j component is the combined mass of car and truck x vj. The result was v = 4.063i + 93.19j ft/s

What I'm having trouble with is determining the position. What I've tried to do is use conservation of energy in each direction 0.5v^2 = μgd, where v is each component and I solve for di and dj in two separate instances which did not work. I also tried to to use the magnitude of the velocity instead, solve for magnitude of d, then use the angle between the two velocity components to determine the components of distance. I can't seem to determine the method so any help is appreciated.

 

[haruspex]

where v is each component and I solve for di and dj in two separate instances

That is not going to work. That would produce the same answer whether the wreckage moved in a straight line to its destination or moved first in the x direction then in the y direction (which would clearly cost more frictional energy).

use the magnitude of the velocity instead, solve for magnitude of d, then use the angle between the two velocity components to determine the components of distance.

That should do it.