# Homework Help: Proving the Possibility of a Collision (Legal Puzzle)

1. Sep 20, 2011

### GoldenGod

Hi. I'm I law student in my fourth year. We have a subject called Practice Court wherein we are trained and taught how to act as lawyers in court.

Now here's the problem, the case that was assigned to us was about a vehicular accident. In our defense, I suggested a very ridiculous and difficult defense to prove that our client's bus was not the party who bumped the complainant's minibus. I am tasked with proving the possibility of version of what really happened by explaining it using physics. I'm not really a physics expert but I understand a little of it during my high school days. Here is our version:

Our clients bus (vehicle C) was at full stop at the other side of the street. Complainants minibus (vehicle B) was also at full stop. Suddenly another bus (vehicle A) bumped the left rear of the minibus. It caused vehicle B (the front right side of B) to slide and hit the concrete post, spin by 140-180 degrees then slip/skid towards our clients bus.

Now, my question is, is our version of the story possible given the following circumstances:

1. Vehicles A and C are city buses having a weight of 25,000 to 30,000 pounds.
2. Vehicle B is an L300 Mitsubishi Vehicle with a weight of 3,704 pounds.
3. When the collision between A and B happened, B's driver wasn't stepping on the brakes or does not have his handbrake on.
4. B's tires are worn out.
5. It was heavily raining and the road was slippery.
6. The distance between B and C before the first collision happened is around ten (10) meters.
7. A's acceleration and velocity is the top speed that a city bus can go. (150km/hr maybe)

I would really appreciate all the help that you can give in answering this puzzle. You can add additional assumptions. Attached herein are four photos that can show you the situation. Thanks in advance.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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Last edited: Sep 20, 2011
2. Sep 20, 2011

### PeterO

If your defense is based on a bus in the city doing 150 km/hr I think you are in trouble. Over what distance must a city bus accelerate in order to reach that speed, and what was between the point that far away and the location of the first collision. There will have been a few hundred witnesses happy to testify about the incredible sight of the speeding bus. Also, the 60cm thick layer of mangled metal - which was previously a Mitsubishi L300 - attached to the front of Bus A will testify to the veracity of that fanciful scenario.

3. Sep 21, 2011

### GoldenGod

The complainants lawyers are dumb at physics so they won't probably be able to raise a question about the distance needed to achieve 150km/hour velocity.

I was thinking if it's possible for vehicle B to slide when vehicle A bumps it, hit the concrete post, spin by 140-180 degrees then slide towards vehicle C. I've done all the assumptions to reduce friction and increase the force coming from the first vehicle (A) but still would our scenario be possible?

I'm not a physics major but I plan to check the formulae available on the net for computing the possibility of this event. Still, I'd appreciate all the help.

Oh, thanks for the comment Peter for the comment about the acceleration. I'll prepare a counter-argument for that in case they ask it on cross-examination.

4. Sep 21, 2011

### PeterO

I would hope that the complainants lawyers are smart enough to realise that a bus in the city will not be travelling at 150km/h. And I am amused at your reference to a bus travelling at 150 km/h "bumping into" the minibus.

5. Sep 30, 2011

### GoldenGod

Actually, they accused our client of bumping them at 120 kph. So i thought they'd think that its possible for the colliding bus to run at a speed of 150 kph. I'm more concerned with the possibility of the minibus bouncing into the concrete post, turning 140-180 degrees then bumping at vehicle C.

I need some help computing the speed of the minibus (vehicle B) after vehicle A collides with it and the speed of the minibus after it collides with the post.

I only know the basic f = ma. T_T

Last edited: Sep 30, 2011
6. Sep 30, 2011

### PeterO

If they said your client was travelling that fast, it would be easy to test.

120 kph is around 33 m/s.

If your clients bus collided in a way to cause 2g acceleration [you client would be pretty badly injured of that happened], it will take about 1.6 seconds to stop. The average speed will have been 16.5 m , so your clients car will finally have stopped 26 metres down the road.
If your client merely bumped, and used the vehicle brakes to stop, he will have achieved about 0.5 g acceleration. That means over 6 seconds to stop - with the same average speed - so will have finally halted 100m down the road.
Where did the minibus stop?

btw, the 150km/h bus won't have stopped for way over 100m, and will have blocked the minibus from getting back to the other side of the road and hit the other bus after "bouncing off the power pole".