Robert Harris offers a closely reasoned answer to that question, complete with a cool GIF of the Zapruder film to buttress his argument.
“I have been writing about this for many years, but I may not have been as clear as I should have been. There is in fact, a very easy way to confirm that Lee Oswald could not have fired all the shots during the assassination.
“To understand it, one needs to first ask why the passengers in the limousine reacted as they were seen doing in the Zapruder film, running at full 18.3 frames per second.
Harris goes on:
“The evidence which answers that question is as follows:
“1. The Warren Commission concluded that ‘a substantial majority of the witnesses stated that the shots were not evenly spaced. Most witnesses recalled that the second and third shots were bunched together.’
“2. Dr. Luis Alvarez concluded that there was a loud and startling noise at frame 285, but suggested that it was a ‘siren.’
3. In Dec. of 1994 Dr. Michael Stroscio, another brilliant physicist who has chaired Presidential science commissions, wrote a paper, suggesting that the noise at 285 was the gunshot which missed the President and went on to cause James Tague’s minor wound.
“4. The visible reactions were carried out by every surviving passenger in the limo, all beginning in the same 1/6th of one second, during frames 290-292. (Alvarez identified Zapruder’s reaction at frames 290-291)
5. Roy Kellerman said the final shots came in a “flurry.”
6. Bill Greer said “The last two seemed to be just simultaneously, one behind the other.”
7. Mrs. Connally said she heard a single shot, then looked back at the President, which we see her do at about frame 258, then heard the shot that she thought, wounded her husband, followed by the fatal head shot.
8. Mrs. Kennedy said she heard a single noise, then two shots after Connally began to shout, which he did at approximately frame 240.
9. Experts are unanimous that involuntary startle reactions must begin within no more than 1/3rd of a second (6 Zapruder frames). Therefore, the shot which provoked the reactions at frames 290-292, could not have been fired any earlier than frame 285, which is 1.5 seconds prior to the headshot at frame 313.
10. Tests conducted by the FBI and the HSCA have proven that it was impossible to accurately fire the alleged murder weapon twice within 1.5 seconds.
Harris concludes: Oswald might have fired one of the shots at 285 or 313 but he could not have fired both.