Question

1.1 Context

Horatio Leafbottom, a newly initiated member of Gangster’s Union Local No. 219, was shot in the shoulder at a recent union meeting for refusing to apologize after making a strong comment on the topic of superiority of cats as pets. Luckily, the bullet traveled straight through Leafbottom’s shoulder. He will make a full recovery. Because of the chaos at the time, however, Leafbottom cannot make a confident determination of the shooter’s identity. Police investigators have narrowed the suspect field to the three candidates who were armed and in the room at the time. Janice Jackson, a small-time software pirate, was found carrying a .38 Special. Aloisius Datarcy, a suspected weapons dealer, was found with a .45 Automatic Colt Pistol (ACP). Merv Redwood, suspected money launderer, was apprehended with a .357 Magnun. All three guns had been fired recently. Neither the bullet nor the shell casing was found at the crime scene. However, based on Leafbottom’s testimony, you can pin-point where in the room Leafbottom was standing when he was shot. Further, the emergency doctor’s report indicates definitively that, based on entry and exit wound locations, the bullet emerged from Leafbottom’s shoulder with a perfectly horizontal velocity. The bullet left Leafbottom’s shoulder 1.6325 m above the ground. The hole in the wall was centered 1.627 m above the ground, 5.5 mm below Leafbottom’s exit wound, and 3 m behind Leafbottom.

1.2 Potential Scenarios

1. Janice Jackson shot Leafbottom with a .38 Special

2. Aloisius Datarcy shot Leafbottom with a .45 ACP

3. Merv Redwood shot Leafbottom with a .357 Magnum

1.3 Background Information

FBI firearm expert Lorenzo Nofingers has provided you the following information showing estimated muzzle velocities based on the firearms confiscated from the suspects.

1. .357 Magnum - 442 m/s muzzle velocity

2. .38 Special - 300 m/s muzzle velocity

3. .45 ACP FMJ - 250 m/s muzzle velocity Further, ballistics testing indicates that passing through Leafbottom’s shoulder would slow each bullet down to 30% of its initial muzzle velocity. You may refer to this observation on your final report.

1.4 Assignment

You must assist the police in identifying the shooter and provide a detailed justification in your report for the police, district attorney, and for the lead editor of Gangster Today magazine.

Answer 1

According to the information provided, there is substantial evidence pointing towards one of three persons of interest, Janice Jackson, which makes her the suspect in this scenario. Using the application of physics dealing with projectile motion, it is possible, using the information given, to identify the gun that was used to shoot Horatio Leafbottom. By using the vertical motion equation, yf = yi + yi,yt + (1/2)gt2, I applied the information provided (gravity, exit height, final height) to find the time it took for the bullet to travel, shown below:

1.627-1.6325 = (1/2)(-9.8)t2
-0.0055/-4.9 = -4.9t2/-4.9
t2 = 0.00112
t = 0.03347

With this information, I then found the final horizontal velocity using the horizontal motion equation, x = vi,xt, by using the distance the victim was standing from the wall as x, and the time found using the vertical motion equation:

3 = (vi,x)(0.03347)
Vi,x = 89.63251

Specific information about the three handguns found was provided by FBI Firearm Expert Lorenzo Nofingers about the firing speed of each type of gun:

FBI Muzzle Velocities
Firearm Muzzle Velocity (m/s)
.357 Magnum 442
.38 Special 300
.45 ACP FMJ 250

By using this information, and the fact that a bullet is slowed down by about 30% (as shown by the ballistics testing provided), I calculated the average speeds of each bullet to see which was closest to the final velocity I found in the above equations. Person of interest Merv Redwood’s gun fired at 250 m/s, and the final velocity of his supposed bullet was 75 m/s, taking him off the list, as well as Aloisus Datarcy, whose gun fired his supposed bullet at 132.6 m/s, leaving the final person of interest, Janice Jackson, the only possible suspect. The final speed of her bullet, when the 30% ballistics factor is counted, was 90 m/s, almost matching the mathematical final velocity I previously found, which is why it is my belief that Janice Jackson is the unsub (unknown subject) in this case.