I hope you already know you shouldn’t believe every crazy-awesome thing you see on the internet; there’s a lot of fake stuff out there. But don’t worry, it’s possible to use physics and video analysis to see what’s real and what’s not.
In this case, some guys tweeted out this cool-looking soccer trick: One dude kicks a ball toward a wall that has an outline of a soccer goal on it, with two holes in the upper corners. At the same time, another guy tosses a ball from the side, and when the balls collide, they ricochet into the holes like billiard balls. It looks magical. Alas, it’s fake. If you look closely, you can see a cloud make a weird move, indicating a video edit (as spotted in an observant tweet).
But it’s more than just glitchy clouds. This soccer trick also breaks some physics rules. Really, this is the fun part—using some fundamental ideas to show that the video is fake.
I’m going to start with the ball that’s tossed from the the side. I can easily measure the motion of this one because it’s moving across the camera’s field of vision. Using the Tracker video analysis tool, I can mark the horizontal and vertical location of the ball in each frame of the video. Also, by looking at the frame rate, I can put a time stamp on those coordinates.
With that, I get the following plot of horizontal position vs. time for the tossed ball:
The key thing to see here is that the data is linear. This means the ball moves in the horizontal direction with a constant speed (which is the slope of the line). I get –6.844 m/s (about 15.3 mph). Is that OK? Well, if you throw a ball, there is only one force acting on it after it leaves your hand (assuming it’s going slow enough to ignore air resistance), and that is gravity. Since the gravitational force pulls only in the downward direction, it doesn’t affect horizontal velocity. With no horizontal forces, there’s no change in horizontal motion. So this checks out.
What about the vertical motion? The downward-pulling gravitational force depends on the mass of the object as well as the local gravitational field (g = 9.8 newtons per kilogram). Since the vertical acceleration also depends on the mass, free-falling objects will all move with the same acceleration—no matter what the mass. This vertical acceleration has a value of –9.8 m/s2. Now, how do you measure the acceleration of a soccer ball from the video? If an object has a constant acceleration, then its position should agree with the following kinematic equation:
If I fit a quadratic equation to the position data, I can find the coefficient in front of the t2 term. This coefficient should be equal to half of the acceleration (if the kinematic equation is true—and it is). Let’s do it. Here’s what I get:
The quadratic fit for this data gives a t2 coefficient of –7.00 m/s2. This means the ball has a vertical acceleration of –14.0 m/s2—instead of –9.8 m/s2 like normal objects on the surface of the Earth. Yes, there can be some error in these kinds of calculations, but this one seems too extreme to be a mistake. I suspect it’s a real ball, but its motion was played back at a higher speed so it could look like it’s meeting up with the kicked ball at the right place.
Crash Course on Collisions
But wait! There’s more. What about that collision? When the two balls interact, there is a force pushing them apart. Because of the nature of forces, this force pushes with an equal magnitude (but opposite direction) on the two balls. So, the kicked ball pushes on the tossed ball, and the tossed ball pushes back on the kicked ball. Since forces change the momentum of an object, the two balls have equal but opposite changes in momentum. Oh, momentum (p) is the product of mass and velocity. Like this:
There’s another common way to think about momentum with collisions: The change in momentum of the kicked ball is opposite that of the tossed ball. This is the same as saying the total change in momentum is zero. Thus the total momentum (for both balls) before the collision must be the total momentum after the collision. Yes, momentum is a vector—it has components in all three dimensions. However, we can consider just one direction at a time to make things simpler. Let’s look at the momentum of the balls in the horizontal direction (the direction the tossed ball is moving).
Let’s start with an example using some simple numbers for momentum, just so we can see what should happen. Suppose the tossed ball is moving in the negative-x direction with an initial momentum of –10 kg×m/s (yes, that’s the correct units for momentum). After the collision, say it bounces back with a momentum of +5 kg×m/s. In order to conserve momentum, the kicked ball must recoil with a momentum of –15 kg×m/s (since –15 + 5 = –10, just like before the collision).
But wait! There’s something else to consider in a collision—kinetic energy. Kinetic energy also depends on mass and velocity, just like the momentum. However, kinetic energy is a scalar quantity. It can be calculated as:
Notice that since the velo