Car crashes, I try to analyze it.

[Ziyonex]

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.

 

[edgepflow]

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.

 

[Ziyonex]

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?

 

[edgepflow]

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.

 

[Danger]

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.