# Two cars traveling toward each other question

## Main Question or Discussion Point

An ongoing argument that i can't seem to settle.

Say two identical cars with the same total weight are traveling at each other at 100km/h and hit head on.

Would this be the same as one vehicle hitting a brick wall at 100km/h or would the speeds combine and come to 200km/h?

Assume that the brick wall will "give" or crush to the same degree as the crumple zone of the cars (or simpler, assume in the second example one vehicle strikes another one that is backed up against an immovable brick wall).

Related Other Physics Topics News on Phys.org
Nice question !
It's the same, because of the conservation of momentum, the two cars will be at rest right on, exactly similar to the case a car hit the brick wall.

From this example, we can see that in a head on crash, the heavier the car, the less risk for the driver because the final velocity will still be on the same direction with the heavier car. The smaller car will be smashed back.

soo they will just hit each other and the energy won't become like a car running into a brick wall at 200km/h

dst
In opposing directions? It's the equivalent of hitting a brick wall at 200kmh. Let's change the reference point in space to one of the cars, and let's say this car is stationary relative to everything else. Then, the other car is already approaching at 100kmh, and also, because of the shift in reference point, the speed of the newly stationary car has to be added onto the opposite side.

Danger
Gold Member
Let's put it this way: if some idiot driver does something to cause a collision, I'd sure rather T-bone him than hit head-on.

In opposing directions? It's the equivalent of hitting a brick wall at 200kmh. Let's change the reference point in space to one of the cars, and let's say this car is stationary relative to everything else. Then, the other car is already approaching at 100kmh, and also, because of the shift in reference point, the speed of the newly stationary car has to be added onto the opposite side.
The velocity of one car in the other car's reference is 200km/h, but the impact is just similar to the 100km/h smash into a brick wall because the 2nd car is not a firmly standstill object like the wall.

In the case where you assume a perfectly inelastic collision, there is no difference between hitting a solidly built, unyielding, brick wall or an identical car travelling toward you at the same speed.

If the brick wall yields a bit, again assuming perfect inelasticity, you're better off hitting the brick wall.

In the real world, collisions are always at least slightly elastic.

Danger
Gold Member
I saw that Mythbusters, Chug. Cool work-up to the final act. I am retracting my previous statement because I missed out on a serious factor in the initial post. It specified a head-on collision, which I somehow overlooked. I stand by my opinion that T-boning a car is better than hitting it head-on, simply because it will crumple differently, but that wasn't part of the original question. My apologies if I misled anyone.

I saw that Mythbusters, Chug. Cool work-up to the final act. I am retracting my previous statement because I missed out on a serious factor in the initial post. It specified a head-on collision, which I somehow overlooked. I stand by my opinion that T-boning a car is better than hitting it head-on, simply because it will crumple differently, but that wasn't part of the original question. My apologies if I misled anyone.
It was pretty interesting. And I thought of your orginal comment as a funny statement, so no harm done. haha

Danger
Gold Member
I thought of your orginal comment as a funny statement, so no harm done. haha
That is my ideal world, where stupidity is mistaken for humour.

In opposing directions? It's the equivalent of hitting a brick wall at 200kmh. Let's change the reference point in space to one of the cars, and let's say this car is stationary relative to everything else. Then, the other car is already approaching at 100kmh, and also, because of the shift in reference point, the speed of the newly stationary car has to be added onto the opposite side.
Only if the wall ends up traveling at 100 km/h in the original direction of the 200 km/h car. Make sure you do a complete Galilean transformation, not just half of one. It's the change in speed that determines how much energy is dissipated in the collision.

Both cars are moving in opposite directions (ie towards each other). Lets say that one car is CAR A and the other car is CAR B, now according to te rules of finding the relative velocity of any object against any other object we find that the relative velocity of car A to car B is 200 Km/h and vice versa. now , for the same effect (ie same amount of damage TO ONE OF THE CARS (say car A) will be equal to a variable "X". But the total damage of the whole system (ie to both of the cars) will be 2X.

Agreed ?

Now , as the wall is stationary therefore the speed of the car should be 200Km/h so that the damage is equal to the TOTAL DAMAGE IN THE SYSTEM (ie previously equal to both cars ). But if you just want that the car should be damaged EQUAL TO ONE OF THE CARS ( ie car A) then car A should move at 100Km/h.

Now this explaination is only valid in the case that all other influences are kept constant. For eg : there should be no wind, no water molecules to disrupb the experiment. ETC.

Not only is it the same force, but its the same situation. Neither reference is more valid than the other. One car traveling 100km/h hitting another car traveling 100km/h and one car traveling 200km/h hitting another car at "rest" are two different descriptions of the exact same event.

Danger
Gold Member
One car traveling 100km/h hitting another car traveling 100km/h and one car traveling 200km/h hitting another car at "rest" are two different descriptions of the exact same event.
Rethink, pal. I know that it is counter-intuitive and hard to accept, but a car hitting another car at 100 km/h has the same reaction whether that other car is stationary or closing at an additional 100 km/h. I sure as hell don't like it, but that's how it is.

Both cars are moving in opposite directions (ie towards each other). Lets say that one car is CAR A and the other car is CAR B, now according to te rules of finding the relative velocity of any object against any other object we find that the relative velocity of car A to car B is 200 Km/h and vice versa. now , for the same effect (ie same amount of damage TO ONE OF THE CARS (say car A) will be equal to a variable "X". But the total damage of the whole system (ie to both of the cars) will be 2X.

Agreed ?

Now , as the wall is stationary therefore the speed of the car should be 200Km/h so that the damage is equal to the TOTAL DAMAGE IN THE SYSTEM (ie previously equal to both cars ).
No. KE = 1/2 mv^2; if a single car hits a wall at 100 km/h, the KE dissipated is 1X, if it hits the wall at 200 km/h, the KE is 4X. To get the same total KE as the two car collision, the single car would have to hit the wall at 141.4 km/h.

Not only is it the same force, but its the same situation. Neither reference is more valid than the other. One car traveling 100km/h hitting another car traveling 100km/h and one car traveling 200km/h hitting another car at "rest" are two different descriptions of the exact same event.
Yes. The key is the speed change during the event; if a car traveling at 200 km/h hits another at rest, the final speed of both cars is 100 km/h, which gives a difference in speed of 100 km/h for both cars and the same energy dissipated as in the two cars at 100 km/h each.

Rethink, pal. I know that it is counter-intuitive and hard to accept, but a car hitting another car at 100 km/h has the same reaction whether that other car is stationary or closing at an additional 100 km/h. I sure as hell don't like it, but that's how it is.
Danger, you don't need to like it 'cause it ain't true! If the single car hits a stationary car, the final speed of the conglomeration is 50 km/h.

Last edited:
@mender.....if u would have read my post properly X does NOT REPRESENT ENERGY....it represents the amount of damage..........DAMAGE

Danger
Gold Member
Danger, you don't need to like it 'cause it ain't true! If the single car hits a stationary car, the final speed of the conglomeration is 50 km/h.
I must be missing something here. By my reckoning, the final speed will be zero in any measurement system.

@mender.....if u would have read my post properly X does NOT REPRESENT ENERGY....it represents the amount of damage..........DAMAGE
Dissipating KE is what causes DAMAGE, so knowing the KE dissipated tells you how much DAMAGE there is; therefore 4X KE = 4X DAMAGE.

I must be missing something here. By my reckoning, the final speed will be zero in any measurement system.
Unless the stationary car is backed by an immovable brick wall, it will be accelerated by the collision in the same manner that the moving car will be decelerated by the parked car. If the cars weigh the same, both cars will end up at the average of the two initial speeds. Eventually the skidding tires bring both cars to a stop but that will be well after the initial impact.
... but a car hitting another car at 100 km/h has the same reaction whether that other car is stationary or closing at an additional 100 km/h.
In a momentum exchange, (Va+Vb)/2 =Vfinal if both objects have the same mass. So (100km/h + 0 km/h)/2 = 50 km/h. To get a Vf of 0, the speeds have to cancel, so car B has to moving at 100 km/h. The speed of car B is as much a factor as the speed of car A. So given a choice, hit the parked car rather than the vehicle coming at you head-on, especially if that vehicle outweighs your vehicle!

It's always the speed relative to each other just before the collision that is important. A NASCAR running at 150 mph and hitting the back of a slower car going 100 mph is the same as a 50 mph car hitting a stopped car.

Last edited:
In fact we can define the speed of the two moving bodies to be whatever we want.

Say you are floating in space and witness two asteroids heading towards each other at a constant speed (100 mph) about to collide from your frame of reference.

From asteroid a's reference, it is at rest and the oncoming asteroid b is coming towards it at 200 mph.

From the reference of a spaceship travelling 1000 mph in asteroid a's direction, asteroid a is moving in the opposite direction at (-)900 mph, and asteroid b is moving its original direction at 1100 mph.

From a space frog on planet ulek's reference...you get the point.

None of these observations are the "correct" one because all motion is relative.

The individual speed of the moving bodies can be arbitrarily defined to whatever we want, the only thing that is constant is the total speed of the two moving bodies relative to one another.

Thus when you have two scenarios where the individual speed varies but the total speed is the same, it is essentially the same event happening from a different reference, so of course the force (damage) will be the same.

Right. And since all motion is relative, you can say that either one was moving and the other stopped. That also means that you can arbitrarily decide which object has the KE that gets dissipated in the collision.

A lot like saying that a windmill is powered by the ground pushing it through the air instead of the more common ground based frame of reference definition of wind. The energy source is dependent on the FOR.

are you assuming an inelastic or an elastic collision?