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h2. Part A

A 4460 lb Ford Explorer traveling 35 mph has a head on collision with a 2750 lb Toyota Corolla, also traveling 35 mph.  Assuming that the automobiles become locked together during the collision, what is the speed of the combined mass immediately after the collision?

System:  Explorer plus Corolla as [point particles|point particle].  External influences will be neglected, as we assume that collision forces dominate.

Model:  [Momentum and Impulse].

Approach:  We begin by sketching the situation and defining a coordinate system.


Since we assume that external forces are negligible during the collision, we set the external impulse to zero which gives:

{latex}\begin{large}\[ p^{TC}_{x,i} + p^{FE}_{x,i} = p^{system}_{x,f} \]\end{large}{latex}

or, in terms of the masses:

{latex}\begin{large}\[ m^{TC}v^{TC}_{x,i} + m^{FE}v^{FE}_{x,i} = (m^{TC}+m^{FE})v_{x,f} \]\end{large}{latex}

which gives:

{latex}\begin{large}\[ v_{x,f} = \frac{m^{TC}v^{TC}_{x,i} + m^{FE}v^{FE}_{x,i}}{m^{TC}+m^{FE}} = \mbox{3.71 m/s} = \mbox{8.3 mph}\]\end{large}{latex}