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If I use the equation for projectile motion and know the range and angle debris was launched from a car accident, can I find the speed of the car? For example a car crashed into a wall and bricks were projected a known range with a known angle.

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  • $\begingroup$ How do you think this information would tell you the speed of the car? $\endgroup$ Commented Feb 26, 2018 at 6:05
  • $\begingroup$ From the initial velocity needed to project the object a known range $\endgroup$
    – Alex
    Commented Feb 26, 2018 at 10:50

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Given only data on a single object(projectile) from a crash, I don't think you can. Honestly, to me, this sounds more like a problem involving inelastic collisions and a momentum triangle. Given my knowledge and what you have given in the question, the brick would also have to be the only debris ejected from the crash. I can't give numbers right now because I don't have access to a pencil and paper.

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If there are exactly two pieces of debris, and you know the masses of both + the mass of the car, then yes, it's doable. You can compute the total momentum of the debris and reconstruct the momentum of the car using conservation of momentum. Dividing by the mass of the car gives the result.

If there are more than two pieces of debris, then you'll need to know the masses and velocities of all of them. It makes the calculation more complicated, but in principle, you can repeat the above computation.

As described in the question however, the answer is 'no'. You also need to know the speed (and mass) of the remnant of the car, which qualifies as a piece of debris.

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  • $\begingroup$ If you neglect the bond needed to essentially break the brick from the wall, would it’s initial launch velocity to a known range not be equal to the speed of the car at the instant after the crash? $\endgroup$
    – Alex
    Commented Feb 26, 2018 at 10:55
  • $\begingroup$ I don't understand your question. What do you mean by "bond"? What are you referring to when you say "launch velocity"? $\endgroup$
    – Allure
    Commented Feb 26, 2018 at 10:58
  • $\begingroup$ When I say bond I refer to the mortar in the wall or the cement required to hold the bricks together. (The brick is not under tension) So it’s assumed to be 0. $\endgroup$
    – Alex
    Commented Feb 26, 2018 at 11:42
  • $\begingroup$ When I say launch velocity I’m referring to the velocity needed to project a projectile a known range in the projectile motion equation. $\endgroup$
    – Alex
    Commented Feb 26, 2018 at 11:44
  • $\begingroup$ I see. No, because momentum is conserved. The equation is $m_1v_1 = m_1v_1' + m_2'v_2'$, and you only know two of the variables on the right hand side (the mass of the car and the speed of the brick). You need also the mass of the brick and the speed of the car. $\endgroup$
    – Allure
    Commented Feb 26, 2018 at 11:44

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