Conservation of momentum proves Lee Harvey Oswald did not kill JFK

First watch the stabilized Zapruder footage of the shot.
Note how JFK's head moves backwards.

The one-dimensional Law of conservation of momentum states:

I used the symbol "v" for the bullet's velocity, "u" for the velocity of JFK's head, and "x" denotes the horizontal axis in the video.

If we work in the reference frame of the car, then the velocity of JFK's head before the interaction is zero, so:

The part of JFK's head that comes off is relatively small, so we assume the mass of the head remains constant. The dominant energies involved in the interaction will be the kinetic energies of the head and bullet, so we ignore the heating of the head and bullet, and the internal kinetic energy of the brain etc, and therefore treat the interaction as an elastic collision.

Energy conservation then gives:

The solution to these two equations is well known, see the (always excellent) Farside teaching notes. The velocity of the bullet before the collision is:

We already know from watching the video that the velocity of JFK's head (symbol "u") after the interaction is negative (i.e. in the backward direction). We also know the masses are positive. Therefore, according to the above equation, the velocity of the bullet before the impact can only be negative. In other words, the bullet approached from the front of the car.
Since Lee Harvey Oswald was in the book repository behind the car, he could not possibly have shot JFK.

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