Cycle 4 In-class Project: Forensic Investigation of JFK’s Assassination

On November 22nd 1963, ay 12:30pm, President John F. Kennedy (JFK) was traveling in a motorcade in Dallas’s Dealey Park when he was fatally shot by Lee Harvey Oswald. Oswald, shooting from the 5th floor of the Texas School Book Depository, fired three shots, one of which passed through Kennedy’s neck and one through his head. Kennedy died 30 minutes later at Parkland Hospital. A 10-month investigation conducted as part of the Warren Commission concluded that Oswald was the sole gunman responsible for the assassination.

However, to this day there remains controversy and skepticism over the Commission’s findings, and numerous conspiracy theories have been proposed. The motives of Oswald, a former US Marine who defected to the Soviet Union, were never determined, as he was shot and killed two days after the assassination by Jack Ruby, a Dallas nightclub operator. Ruby was convicted and sentenced to death, but his conviction was overturned; and before a retrial could be scheduled a few years later he died of a pulmonary embolism (a common ailment at a time of pervasive smoking). In 1979, the US House Select Committee on Assassinations (HSCA) proposed that a second shooter was involved, and that the assassination was therefore a conspiracy. While the evidence suggesting a “second shooter on the grassy knoll” was shown to be incorrect in 1988, conspiracy theories continue to be widely held, being the subject of numerous books, films and websites. As recently as 2013, 60% of Americans believe a conspiracy was involved in the assassination of JFK (Gallup poll, 2013).

As a forensic investigator, you are charged with reviewing the evidence of the JFK assassination, and in particular assessing the primary physical evidence that has been used to propose the existence of a second shooter: the backward snap of Kennedy’s head just after the final shot strikes him. This is seen in frames 313-319 of the film shot by bystander Abraham Zapruder, who captured the assassination with his home video camera (you can see the relevant frames starting at time 1:40 at this link: https://youtu.be/GL1qSGk8oMQ?t=1m40s). Numerous studies, including the HCSA, point to this motion (about 1.6 ft/s = 0.50 m/s) as evidence of a second shooter in front of JFK’s car, since a bullet should have propelled the head backward (the “ballistic pendulum” theory). However, in 1976 Nobel Prize-winning physicist Luis Alvarez proposed an alternate theory, that the expulsion of skull and cranial tissue from the forehead as the bullet shot by Oswald from behind exited the head was enough to propel the head back toward Oswald (the “jet” theory). Your job is to use conservation of momentum and energy to examine both theories and determine if the head motion proves the existence of a second shooter or not.

The solution you turn in should address the following three (3) questions:

Question 1: Use the “ballistic pendulum” model to determine the velocity (speed and direction) of Kennedy’s head if the bullet had come from “the grassy knoll” (second shooter), and calculate how much energy would have been dissipated as a result. Model the collision as one in which the bullet enters at the front of the head (from “the grassy knoll”) and has a perfectly inelastic collision, and use this to compute the final head speed and direction. Compare this number to the estimated head speed from the Zapruder film, 0.50 m/s. Compute the energy lost as a fraction of the initial (kinetic) energy of the bullet.

Question 2: Use the “jet” model to determine Kennedy’s head velocity (speed and direction) using specific assumptions about the fraction of skull/cranial tissue dispersed and energy lost in the interaction? Model the collision as one in which the bullet enters from behind the head (the direction Oswald had fired at Kennedy) and exits at the front, with some fraction of the skull/cranial tissue travelling outward with it. The fraction of tissue lost and the fraction of energy dissipated are listed in the Table below – use the values listed for your team in your calculation (we will be synthesizing the numbers from all cases as a class). Use both momentum and energy conservation relations, and compare your speed to the estimated head speed from the Zapruder film, 0.50 m/s.

% of skull and brain % energy lost to Team tissue ejected with heat in jet model bullet in jet model Electron/Graviton 5% 90% Proton/Neutron 5% 80% Up quark/Down quark 10% 90% Strange quark/Charm quark 10% 80% Bottom quark/Top quark 15% 90% Neutrino/Photon 15% 80%

Question 3: Make a determination: is a second shooter necessary to explain the movement of Kennedy’s head after he is shot? While the second shooter hypothesis has had many adherents, is it necessary to explain this particular aspect of the Kennedy assassination? Base your answer on your calculations above for the two models of the bullet-head collision, and be sure to consider to what degree the bullet- head system is an isolated one (i.e., do tension forces with tendons and musculature in the neck matter? If so, how so?). You may also consider any other relevant information from the event.

Each piece of your solution will be built up in our training problems; you should not have to spend significant time outside of class to complete this assignment. Your team’s job is to compile the pieces together and apply them to your particular case parameters to come up with your final determination in this case. The completed solution sheet, signed by all members of your team, should be submitted to the assignment link in the Cycle 4 Project folder by 11:59pm on Monday, November 23rd (note: 52 years and 1 day after JFK’s assassination). A hard copy of your solution should also be turned in during your Monday or Tuesday class meeting.

Relevant Links: • Wikipedia entry on the Assassination of JFK: https://en.wikipedia.org/wiki/Assassination_of_John_F._Kennedy • Wikipedia entry on JFK Assassination Conspiracy Theories: https://en.wikipedia.org/wiki/John_F._Kennedy_assassination_conspiracy_theories • Zapruder film: https://www.youtube.com/watch?v=GL1qSGk8oMQ • Alvarez (1976) article on the “jet model”: http://scitation.aip.org/content/aapt/journal/ajp/44/9/10.1119/1.10297 • Report from the Warren Commission: http://www.archives.gov/research/jfk/warren- commission-report/index.html • Report from the 1979 US House Select Committee on Assassinations http://www.archives.gov/research/jfk/select-committee-report/ • JFK Assassination Records Collection: http://www.archives.gov/research/jfk/

Important Numbers for your Calculations: Reported mass of Oswald’s bullets = 160 grains ≈ 10 grams1 Reported speed of the bullets fired from Oswald’s rifle ≈ 2000 ft/sec ≈ 600 m/s1 Brain mass ≈ 1.3 kg2 Total head mass ≈ 4.5 kg3

1 Alvarez (1976), Am. J. Physics, 44, 813 2 Hartmann et al. (1994), Pathologe, 15, 165 3 Yogananadan et al. (2009), J. Biomechanics, 42, 1177