Analysis
In order to analyze our pictures, the first step we took was to measure the distances as shown on the picture below. Using our known length of the Jell-O we can find a scale factor relating the distance on the picture to the real distance traveled by the pellet. We do this by dividing our known length of the Jell-O over our measured distance, which gives us a scale factor for each picture. Using this scale factor we can convert all the distances measured on the picture to the distances that were actually traveled. With those new distances, and our known interval time, we can do some basic calculations to determine the initial and final velocities of the projectile, as well as the deceleration caused by the Jell-O.
Here is an example of what distances we measured on our photo:
Figure 4. Example of analysis (analysis conducted on photo 93).
The equations we used to analyze our photos are shown below. They consist primarily of the basic definitions of velocity and acceleration.
Vi is the initial velocity of the bullet
Vf is the final velocity of the bullet
t is the interval time between images
T1 is the time it takes for the bullet to travel the distance Xi2
T2 is the time it takes for the bullet to travel the distance Xf1
Td is the time it takes for the bullet to travel through the piece of Jell-O
Ad is the acceleration through the piece of Jell-O 