Car crashes, I try to analyze it.

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A user is attempting to analyze a car crash involving a friend who hit a dirt ramp, seeking to calculate the vehicle's initial velocity and time in the air. They measured the ramp height at 1.5 meters and the landing distance at 30 meters, with the ramp angle at 30 degrees. Despite using kinematic equations, they struggle to derive the initial velocity, which was estimated at 18.4 m/s, or about 41 mph, potentially affected by skid marks. The discussion emphasizes the importance of professional accident analysis for legal matters, as online advice cannot be used in court. The user is encouraged to verify their ramp angle and consider the impact of the ramp height on their calculations.
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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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