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Question
Hi, and thank you.  I was hit by an 05 camry at an uncontrolled residential intersection on a very rainy day.  I was traveling Northbound and looked left, looked right(at this intersection you can see more than half a block down), looked left and started toward the intersection at less than 10 mph, looked right again and saw the camry speeding toward my one ton F 350 pick up.  I slammed on the brakes and the car hit my right front bumper  at about mid intersection, changing my direction to NW and I rolled into a hydrant one foot off the curb and brought both of us to a stop. I got a ticket for failure to yield but no ticket was given to the camry who was speeding and hit me.   Granted on such a rainy morning I should have been even more extra cautious.  Please let me know what other information you might need. I so appreciate your time.  I do believe in science.

Answer
Hello patty,

This is a problem for the use of the Principle of Conservation of Momentum. The momentum formula when the 2 objects lock together in the collision is
momentum before = momentum after
M1*U1 + M2*U2 = (M1 + M2)*V
I'll call your truck vehicle #1 and the camry vehicle #2. Whether I use mass or weight will not matter since those units will cancel out when I solve for velocity. I will assume the camry to weigh 3160 lbs and the F350 to weigh 6320 lbs (this is a relatively light weight number chosen from a review of weights for various models of the 2013 F350). With those values, M1=2*M2.

Momentum is a vector, and the direction of the velocities will be a major part of the analysis. I will choose the y axis direction to be the NW direction that M1 and M2 went after the collision. I will focus on the components of the incoming velocity in the x axis direction (which is NE). I will assume neither swerved before collision so that there was a 90 degree angle between incoming velocity vectors. The final velocity, V, has a zero component in the x direction. The components of U1 and U2 in the x direction are
U1x = U1*cos45 = 0.707*U1
U2x = U2*sin45 = 0.707*U2
So the momentum equation considering motion in the x axis becomes
2*M2*0.707*(10 mph) + M2*U2*0.707 = 3*M2*0
Simplifying
2*10 mph = -U2
So the conclusion using the above data is that the camry's speed at the moment of impact was 20 mph.

This is based in assumptions. You said you hit the brakes. Perhaps the Camry did too? A heavier value for the weight of your truck would yield a higher number for U2.

I hope this helps,
Steve

Physics

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Steve Johnson

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I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

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I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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