Two Cars Colliding?

Question

I have a physics question:

Car A is traveling 50 miles an hour east.
Car B is traveling 51 miles an hour east.
Car B hits Car A from behind.

Would the magnitude of the impact be the same if Car B were going 1 mile an hour and hit Car A going at 0 miles an hour?

Answer 1

No. If both were in a vacuum this might be true.

In this world, we have friction. We also have air drafts.

The amount of energy required to travel 51 mph does not necessarily exceed the amount of energy required to travel 50 mph by the same amount as the vehicle going 1 mph.

Taken to an extreme, a vehicle going 18,000 mph would be forced upward into earth orbit. The gravitational pull at 51 mph is hardly measurable but does exist.

I did not do all that well in high school physics, so caveat emptor.

Answer 2

The magnitude of impact will be the same,
but the consequences will be much more severe.

For example in 1 mps / 0 mps collison the car in
front might bounce 1 foot forward and rotate by
10 degrees to the left, but it's no big deal.

In 51 mph/ 50mph the same 10 degrees rotation
might propel the car into the lane of traffic in opposite
direction, and cause huge chain reaction.

Answer 3

I imagine the initial impact would be equal, however the higher speeds of the cars would set into motion a chain of events that would potentially cause more damage.

Of course I'm no physicist.