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Horatio Leafbottom, a newly-initiated member of Gangster's Union Local #219, was shot in the shoulder at a recent union meeting for refusing to apologize after making strong comments on the topic of the 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. Aloisus Datarcy, a suspected weapons dealer, was found with a .45 Automatic Colt Pistol (ACP). Merv Redwood, suspected money launderer, was apprehended with a .357 Magnum. 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 pinpoint 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. After passing straight through Leafbottom's shoulder 1.6325 m above the ground, the bullet travelled another 3 m into the wall 1.627m above the ground.
FBI Firearm Expert Lorenzo Nofingers has provided you with the following table showing estimated muzzle velocities based on the firearms confiscated from the suspects. Investigators on the scene determined that it took the bullet .0335seconds to travel the distance between the victim's shoulder and the wall. Further, ballistics testing indicates that passing through Leafbottom's shoulder would slow each bullet down to 30% of its initial muzzle velocity. You may reference this information in your final report (Story adapted from APlusPhysics.com).
To calculate the velocity of the bullet as it hit the wall, you will use the horizontal distance the bullet traveled and the time that investigators calculated it took the bullet to travel between the victim's shoulder and the wall. For this we will use the formula velocity= distance/time (Hint: The horizontal distance is how far the bullet traveled behind Leafbottom)
The image shows an equation that tells us the final velocity of the bullet. Dividing the horizontal distance the bullet travels (in meters) by the time it takes (in seconds), gives us the final velocity.
Now that you know the velocity with which the bullet impacted the wall, you can use that information to find the final velocity of the bullet. The final velocity of the bullet is 30% of its initial muzzle velocity. Finally, when you have the muzzle velocity, you can determine the weapon used.
he image shows an equation that describes how to calculate muzzle velocity. Taking the final velocity (determined earlier), multiplying that number by one hundred percent, then dividing the total by thirty percent, you can determine muzzle velocity.