Sometimes crazy things happen – so crazy they don’t even seem real. Last week, Phillies right fielder Bryce Harper warmed up before a game with a few practice sticks. He hit a nice practice line, then he collided with another ball in the air. It gives us a fun physics to unwrap. Let’s see how unlikely this event is.
What data can we get from the video?
There are two bullets involved in this crash. Harper has probably started his flight to plate. I’m going to call this ball A. The second ball was thrown at home plate by a player somewhere in the outfield. Let’s call this ball B. I need to get a value to know where the balls start, what their speeds are, and where they collide. The Major League Baseball clip that I’ve linked to before isn’t the best video, in that it doesn’t show the full trajectories of either ball, so maybe we’ll have to just bring us closer to certain things.
One thing we can see is the impact between the two balls, which occurs over second base. Then it looks like the B ball falls straight down and lands near the base. But how high is the point of impact? By watching the video, it is possible to get an approximate free fall time for ball B. (I go with 1.3 seconds, based on my measurements.) If I know the time it takes to fall and the vertical acceleration is – 9.8 meters per second squared (as this happens on Earth), then I can find the fall distance using the following kinematic equation:
With my estimated fall time, I get a collision height of 8.3 meters. If the baseball field is in the xz plane and the position above ground is the y direction, that means I now have the three coordinates of the collision point: x, y, and z. I can use this point to find the throwing speed of ball A. I know it is starting to move at home plate, which is 127 feet from second base. So I’m going to put my origin at home and then let the x-axis be along a line between home and the second.
Now I just need the initial velocity vector for bullet A as it passes through the collision point. There are several ways to find this, but the easiest is to simply use Python to trace the path of the ball and adjust the launch angle until it “hits” the collision. I will use a starting ball speed (egress speed) of 100 miles per hour. (That’s 44.7 meters per second.)