The roads are icy, and you observe a head-on collision on Summit, at the corner with Rhodes: a 1ton car swerves out of his lane and slides through a stop sign at 34mph straight into a 3ton SUV traveling at 13mph in the other direction. The car and the SUV crumple from the collision, and stick together. What is the final velocity, in MPH (you don't need to enter MPH in your answer) , of the SUV/car entanglement (the positive direction is the direction the car was initially going)?

v = -1.3 mph

Explanation:

Assuming no external forces acting during the collision, total momentum must be conserved, so the following condition must be met:

       

The initial momentum is the sum of the momenta of both vehicles, taking into account their relative velocities as they are going in opposite directions. If we take as positive the direction the car was initially going, we can write the following expression:

       

Replacing by the values of the masses of both vehicles and their speeds, we have:

       

This must be equal to the final momentum of the car/SUV entanglement, as follows:

       

Replacing in (3) for the masses, and equating (1) and (3), we can solve for vfinal, as follows:

       

This means that the car/SUV entanglement will move in the opposite direction that the car was initially going.

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