Through random surfing, I found this clip from The Amazing Race (which is apparently some type of reality show). Don’t really know the set up except that it appears some girl is trying to launch watermelons with a slingshot. This looks bad, but she seems to not be seriously injured.
Watermelon smashed on face. Wow. What can I we calculate here? Bring in the video analysis.
How fast was the watermelon going?
First, this is not a very good quality video. The frame rate sucks and there is a very slight panning and zooming (which I will ignore) Second, I really don’t have anything to scale the video so I just assumed the girl-launcher was about 1.5 meters tall. Just a guess. Using Tracker Video analysis, I get the following data (where the x-direction is along the direction of motion of the melon):
This shows the motion of the melon both while being launched and when coming back. The first thing I did was to fit a parabola to the very beginning motion. This will give me the initial acceleration with a value of about 120 m/s2. Zowza.
I can also get an estimate for the initial and final velocity by fitting a linear function to the data. Note – the melon is actually accelerating (due to the gravitational force) but it is moving so fast, I can ignore this. Doing so, I get a launch speed of about 15 m/s and a returning speed of also about 15 m/s (this is good). First, if the melon gets stuck in the launcher then it should have the same return speed that it had launching (energy conservation). Also, 15 m/s seems like a reasonable speed (around 33 mph).
What about the impact?
This is a little bit more complicated. First, there is the initial impact and then there is the recoil of the head. Here is a plot of the head as a function of time (mostly in the direction of recoil)
I guess the first thing to do would be to estimate the acceleration of the head. This is where you would get an injury, if the acceleration was too high. Really, there is only a couple of frames with the head getting hit. I don’t think I can get that from video. But I can get it, oh yes, I can. All I need from the video is the recoil distance. Let me say that the head recoils a distance of 0.2 meters. The other thing I need to know is the final speed of the melon. No clue here. Let me just say that it is going half as fast as it was when it hit (the pieces of the melon are still moving after the collision).
Here is a diagram of the melon at the beginning and at the end of the collision:
Since everything is in the same direction, I can use the scalar-kinematic equation:
Using an initial and final velocity of 15 m/s and 7.5 m/s as well as a distance of 0.2 meters, I get an acceleration of 422 m/s2 (oh, this is the average acceleration). This is about 43 g’s. Clearly enough to smash the melon. What about the head? Does that mean the head had the same acceleration? No. First, it has a different mass. Second, it is connected to the rest of the body so that there are other forces on it.
Perhaps with a better quality video, I could get a little more detail.