# Momentum Theory To Solve Car Crash?

1. Apr 19, 2007

### Gordon Arnaut

I wonder if someone might suggest an approach to solve this problem?

A vehicle weighing 5000 lbs is moving at 10 mph and is struck from behind by a vehicle weighing 5000 lbs and moving at a high rate of speed. The slow-moving vehicle is pushed forward a distance of 150 feet.

How fast was the high-speed vehicle traveling?

I suspect we can apply momentum theory to solve this, but am having trouble getting started.

Regards,

Gordon.

2. Apr 19, 2007

### DyslexicHobo

There is missing information here, unless they want you to solve in terms of something, rather than get a specific answer (which I doubt).

Does it mention anything about a frictional force between the road and tires?

To apply the fact that the slow-moving car traveled 150 feet further than the point of the collision, we would need to know the forces decelerating the moving couplet of vehicles.

By using the equation (m_a)*(v_a) + (m_b)*(v_b) = (m_c)*(v_c), where c = the cars while combined, we can plug in the masses of both objects and the known speed. On the other side of the equation, we'd add the masses and have v_c as an unknown. This is where we run into trouble--two unknowns and no other ways to find them (unless this is not as easy of a problem as I had thought it was). I cannot find any way to solve this problem. Make sure you're supplying all the details.

P.S. Wrong forum. Post it in the homework section.

3. Apr 19, 2007

### Gordon Arnaut

No, this is not an easy problem.

The tire friction was not given, but this is probably something that could be looked up.

I'm not sure it would come into play that much anyway.

Let's take a similar problem, where you have a fast-moving vehicle that hits a boulder and sends it flying through the air. Here the force opposing the movement of the boulder is simply gravity and its inertia.

If we simplify our problem with the two vehicles by assuming one is standing still when it is hit, perhaps we can find a way into it.

Regards,

Gordon.

4. Apr 20, 2007

### rcgldr

Are you assuming that the slower car locked up the tires at the point of collision? If not, the car could have just kept rolling at a slow speed.