2 baseballs collided in an MLB game. How did that happen?

Sometimes crazy things it happened, even the real ones that didn’t seem so crazy. Last week, right-handed Phillies player Bryce Harper was warming up with some practice bats before a game. He hit a nice line, and then he collided with another ball in the air. This gives us fun dissolving physics. Let’s see how difficult this event is.

What data can we get with the video?

There are two balls involved in this accident. Harper probably started his flight home. I’ll call that ball A. The second was thrown by a player on an outside field to the home plate. Let’s call this ball B. I need to get a value to know where the balls start, what their speed is, and where they collide. The Major League Baseball clip I linked to earlier isn’t the best video, as it doesn’t show the full trajectory of both balls, so we’ve had a few roughly enough things.

One thing we can see is the effect between the two pilots, which occurs above the second base. Then it seems that the ball B falls directly and lands near the base. But how far is the point of influence? Watching the video, I can get an approximate fall time for the B. ball (I’m going with 1.3 seconds, based on my measurements.) If I know the fall time and that it’s vertical acceleration – 9.8 square meters per second (because it’s happening on Earth), then I can find the fall distance using the following kinematic equation:

With the calculation of the fall time, I get a collision height of 8.3 meters. If the baseball field is in the xz plane and the position above the ground is in the y direction, that means I now have three coordinates for the point of collision: x, y, and z. I can use this point to find the speed at which A. throws the ball. I know the home plate at 127 feet from the second plate starts to move. So I will put my origin at home and then let the x axis be on the line between the house and the second.

Now I just need the initial velocity vector for ball A to pass through the point of collision. There are several ways to find this, but the easiest way is to draw the trajectory of the Python ball and adjust the angle of the shot until it hits the hit. I will use it initial ball speed (exit speed) 100 miles per hour. (It is 44.7 meters per second.)