Sometimes loopy issues occur—so loopy they don’t even appear actual. Last week, Phillies proper fielder Bryce Harper was warming up earlier than a sport with some observe bats. He hit a pleasant line drive, after which it collided with another ball in midair. That offers us some enjoyable physics to unpack. Let’s see how unlikely this occasion is.
What Data Can We Get From the Video?
There are two balls concerned on this crash. Harper’s in all probability began its flight at residence plate. I’m going to name this ball A. The second one was thrown towards residence plate by a participant someplace within the outfield. Let’s name this ball B. I must get a worth for the place the balls begin, what their velocities are, and the place they collide. The Major League Baseball clip that I linked to earlier than just isn’t the very best video, in that it does not present the whole trajectories of both ball, so we may need to approximate some stuff.
One factor that we are able to see is the impression between the 2 balls, which occurs above second base. Afterwards, it seems that ball B falls straight down and lands close to the bottom. But how excessive above it’s the level of impression? By watching the video, it is doable to get an approximate free fall time for ball B. (I’m going with 1.three seconds, primarily based on my measurements.) If I do know the time it takes to fall, and that the vertical acceleration is -9.Eight meters per second squared (as a result of that is taking place on Earth), then I can discover the falling distance utilizing the next kinematic equation:
With my estimate for the falling time, I get a collision peak of 8.three meters. If the baseball subject is within the x-z aircraft and the place above the bottom is the y path, meaning I now have all three coordinates for the collision level: x, y, and z. I can use this level to seek out the launch velocity of ball A. I do know that it begins shifting at residence plate, which is 127 toes from second base. So I’ll put my origin at residence after which let the x axis be alongside a line between residence and second.
Now I simply want the preliminary velocity vector for ball A such that it passes by way of the collision level. There are a number of methods to seek out this, however the easiest is to simply use Python to plot the trajectory of the ball and modify the launch angle till it “hits” the collision. I’m going to make use of a starting ball velocity (the exit velocity) of 100 miles per hour. (That’s 44.7 meters per second.)