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h2. Part A

Assuming that the automobiles become locked together during the collision, what is the speed of the combined mass immediately after the collision?

h4. Solutions

{toggle-cloak:id=sysa} *System:*  {cloak:id=sysa}Explorer plus Corolla as [point particles|point particle].{cloak}

{toggle-cloak:id=inta} *Interactions:* {cloak:id=inta}[Impulse|impulse] resulting from [external influences|external force] will be neglected, as we assume that the collision is instantaneous.{cloak}

{toggle-cloak:id=moda} *Model:*  {cloak:id=moda}[Momentum and External Force].{cloak}

{toggle-cloak:id=appa} *Approach:*  

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{toggle-cloak:id=diaga} {color:red} *Diagrammatic Representation* {color}

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We begin by sketching the situation and defining a [coordinate system|coordinate system].

|!CollisionInit.jpg|height=175!|!CollisionFin.jpg|height=175!|
||Initial State||Final State||

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{toggle-cloak:id=matha} {color:red} *Mathematical Representation* {color}

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Since we assume that [external|external force] [forces|force] are negligible during the collision, we set the [external|external force] [impulse|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}

{warning}Remember that in our [coordinate system|coordinate system], the Corolla has a negative x-velocity before the collision.{warning}

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