Projectile Motion Video Analysis

What’s the Big Idea‽

Projectile motion occurs when an object simultaneously exhibits both horizontal and vertical motion. Although these motions occur at the same time, they are considered independent. But how can we prove this? In this lab, we use Logger Pro to graph a video of a ball in projectile motion to see how it behaves in the x- and y-directions.

Procedure

The first part of the lab consists of getting our equipment ready and recording an example of projectile motion. To perform the first part of the experiment, we need a meter stick, an iPad, and a ball. First, we lined up the meter stick to the wall to set the scale of the video and prepare it for the video analysis, as shown below.

With that completed, it’s time to film! Projectile motion involves both vertical and horizontal movement, so we throw the ball into the frame of the camera at an angle. Here’s the result:

The second part of the lab is where it gets interesting. After loading the video into Logger Pro, we set the scale of the video, using the measurements provided by the meter stick as a guide. Then, going frame by frame through the video, we plot the center of the ball, as shown below:

Afterwards, we can view the position vs. time graphs. The red dots represent the change in horizontal position and the blue dots represent the change in vertical position.

The shapes of the graphs are the most telling: the change in horizontal position is clearly linear, and the change in vertical position is clearly quadratic. This tells us that no new forces are acting upon the ball in the x-direction and that one consistent force is acting upon the ball in the y-direction, resulting in a gradual change in its velocity.

If we had the velocity vs. time graph, we’d notice that the x-direction would show a completely horizontal line and the y-direction would show a linear graph, indicating a constant acceleration.

Takeaways

So what does all this data mean? What does it show? We know that the original force and velocity can be split up into two separate pieces, one in the horizontal direction and one in the vertical direction. The velocity in the horizontal direction remains constant for the duration of the ball’s flight, however, the velocity in the vertical direction changes, in fact, at a constant rate of -9.8 m/s. Gravity causes the acceleration of the ball downwards, but it only affects it in the y-direction, not in the x-direction as well. These two motions are effectively separate.

However, there are some things that we could have done better in our experiment. Firstly, it would be helpful to record the video a little farther back to see where the ball starts, just for some context. Additionally, having the meter stick in the same plane as the ball while the video is recording (as opposed to measuring the wall) would help eliminate potential sources of error in our graphs. Ultimately, this resulted in strange values for distance in our graphs, none of which made sense. Lastly, we should have saved a version of the graph showing velocity vs. time as well because it would aid in our understanding of projectile motion.