Car crashes, I try to analyze it.

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Discussion Overview

The discussion revolves around analyzing a car crash involving a friend of the original poster, focusing on the kinematics of the incident. Participants explore how to calculate the initial velocity of the car and the time spent in the air after hitting a dirt ramp, incorporating concepts from projectile motion and kinematics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • The original poster expresses frustration in calculating the initial velocity and time in the air after the car hit a ramp, providing measurements of the ramp height, distance traveled, and angle.
  • One participant suggests using a standard kinematic equation for projectile motion, providing a formula that neglects the height of the ramp for a simplified calculation.
  • The original poster calculates an initial velocity of 18.4 m/s (about 41 mph) using the provided formula, questioning its validity given the speed limit and the presence of skid marks.
  • Another participant advises double-checking the ramp angle if the calculated velocity seems low, indicating that a steep angle could affect the results.
  • A separate participant emphasizes the forum's policy against providing legal advice related to real-life accidents, recommending hiring a professional accident analyst instead.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the calculations or the implications of the results. There are differing views on the relevance of the ramp height and the appropriateness of the calculated initial velocity.

Contextual Notes

The discussion includes assumptions about the ramp's angle and the neglect of the ramp height in the initial calculations, which may affect the accuracy of the results. There is also a legal context that participants acknowledge but do not resolve.

Who May Find This Useful

This discussion may be of interest to individuals studying kinematics, those involved in accident analysis, or anyone curious about the physics of projectile motion in real-life scenarios.

Ziyonex
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I feel very stupid right now, but I must figure this out. A friend of mine was in a car wreck; steered off the side of the road and hit a natural dirt ramp. I decided I would try to figure out how long he was in the air for, and how fast he was going initially, but it seems I am just not smart enough, and I'm very frustrated that I can't figure out a simple kinematics problem.

He hit the jump in his car at an unknown velocity. I measured top of the dirt ramp to be about 1.5m from the ground. The car landed about 30m from the edge of the dirt ramp. I measured the angle of the ramp to be about 30 degrees.

I know I have enough information here to calculate all variables in this situation, which is what kills me. If someone could take a few seconds to explain to me how I should go about this, that would be great. I tried two-dimensional kinematics and conservation of energy to try to solve this, but I can't get it.

Driver sustained a minor concussion. Airbag should have deployed, but did not. The enormous Ford Excursion Diesel was totaled.
 
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The 1.5 m tall ramp makes the solution a little more difficult.

However, you can neglect this an get a result that is accurate to within about 7% by using the "level target" standard kinematic solution:

R = vo^2 * sin (2 * angle) / g

x(t) = (vo cos (angle) ) t

where,

R = range = total distance traveled (given)
x(t) = distance traveled as a function of time
vo = initial velocity (solve for)
angle is given.

Try this. If you are interested in including the 1.5m ramp, let me know.
 
The first formula you gave me yielded an initial velocity of 18.4 m/s or about 41 mph. The speed limit on the road was 60 mph, so that seems a little slow, however there were a few skid marks leading up to the dirt ramp, which could account for the reduced velocity.

How did you derive the first formula you gave me?
 
Ziyonex said:
The first formula you gave me yielded an initial velocity of 18.4 m/s or about 41 mph. The speed limit on the road was 60 mph, so that seems a little slow, however there were a few skid marks leading up to the dirt ramp, which could account for the reduced velocity.

How did you derive the first formula you gave me?
The derivation is a little length. See Physics by Tipler under projectile motion.

If the launch velocity seems low to you, double check your 30 deg ramp angle. This is fairly steep.
 
As much as I hate to piss in anyone's cornflakes, the PF policy is to not deal with real-life legal issues. This has arisen several times in the past, and our advice is always to hire a professional accident analyst. It can't be done on-line.
This isn't intended as a put-down, but rather sound legal advice. Nothing that any of us say can be used in court.
 

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