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Question
An 8800 lb. vehicle is traveling straight at 50 mph. A 3300 lb. vehicle is traveling straight at 70 mph and rear ends the first vehicle. How do the vehicles react to crash? ie, will the 8800 lb. vehicle go 20 mph faster? Will the 3300 lb. vehicle continue on?
Thank You in advance.

Answer
The answer to the question depends on how elastic the collision is. I fete collision is completely in elastic (that is the cars stick together after the collision) the final velocity will be given by:
M1*V1+M2*V2=M1*V3+M2*V4
But if the cars stick together after the collision V3=V4 and this becomes:
M1*V1+M2*V2=(M1+M2)*V3
Solving for V3:
V3=(3300*70+8800*50)/(3300+8800)=55.5mph
If the collision is completely elastic (an unlikely scenario) we can assume that the relative velocity after the collision V4-V3 should be equal to the relative velocity before the collision V1-V2:
The relative velocity be fore the collision was 70-50=20 and so the relative velocity after the collision should also be 20:
V4-V3=20
Therefore: V4=20+V3
Solving the momentum equation from above again:
M1*V1+M2*V2=M1*V3+M2*V4
M1*V1+M2*V2=M1*V3+M2*(20+V3)
And solving for V3, the velocity of the first car after the collision:
V3=(M1*V1+M2*V2-M1*V3-20*M2)/M2=41mph
And so the final velocity of the second car V4 after the collision will be:
V4=20+V3=61mph
In the real world the velocitiesr will be somewhere between these two answers.  

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James J. Kovalcin

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.

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