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Homework Help: Would you rather hit another car or a tree?

  1. Oct 30, 2009 #1
    I'm not really a bad student, but I just can't come up with an answer for this question: "You are driving along the highway and encounter an unavoidable situation. You must hit either an identical car moving toward you at the same velocity, or a large tree. Which do you choose?" Obviously, I need to determine which will exert a smaller force. However, because of Newton's third law, the tree will exert an equal force on the vehicle, and so will the other car. Can anyone help me out? Any advice would be appreciated.
  2. jcsd
  3. Oct 30, 2009 #2
    I'm not sure what they are looking for.
    Of course the collision will not be elastic. But in the case of an inelastic collision, your change of momentum is the same in both situations.

    Maybe they want something along these lines:
    The tree is rooted to the ground, so consider it's mass infinite.
    Now consider an elastic collision: what is the change in momentum you'd undergo in each situation?
    I'll leave the math to you of course, but this would indeed lead to preferring one over the other. (EDIT: Sorry, thinking this over again, I am not sure this is true. It looks like they'd be the same as well.)

    Oviously it is the acceleration (force) that matters, not the change in momentum, but it is not really possible with the provided info to calculate anything but the impulse. So you'll probably have to stick to using impulse instead of force.
    Last edited: Oct 30, 2009
  4. Oct 30, 2009 #3
    I believe the question is asking you to consider the total energy in each system.
  5. Oct 30, 2009 #4
    In an inelastic collision, the energy lost by the car is the same in both situations. Remember that in the two car collision, while there may be more total energy, each car gets damaged and each loses the same amount of energy as if it hit an immobile wall.

    I don't think this is a question about energy.
  6. Oct 30, 2009 #5


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    The 3rd law says the force on the tree will equal the force on the car. It doesn't say anything about the relative size of the forces in the tree and two-car collisions. You might arrive at an answer by imagining the two cars hitting opposite sides of the tree simultaneously and then shrinking the tree down to a mere shrub.

    What about the relative width of the tree and car? Would you get more collapse length from one or the other, affecting the duration of the collision? The answer may depend on the design of the car.

    Are you liable for damage to the tree or other car!?
  7. Oct 30, 2009 #6


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    I don't believe this is a homework question. If you hit the other car, then there's a chance that you'll injure/kill an innocent driver, whereas if you hit the tree it is only you that will feel the consequences of your own bad driving.
  8. Oct 30, 2009 #7
    I agree and I think you just answered the question.
  9. Oct 30, 2009 #8


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    One way to answer the question is to consider the other driver, and ignore physics.

    But if we are to take the physics approach, consider the following:

    1. For colliding with the other car, what does conservation-of-momentum tell you about your velocity after the collision?

    2. If the tree is not so large that it may be uprooted or at least knocked over in the collision, what does that tell you about your velocity after the collision?

    Of 1 and 2, which result is more desirable from your point of view?
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