Home Run Height

I was at a Chicago Cubs baseball game last summer and was lucky enough to see all-star shortstop Javier Baez hit his longest home run of the season.  Baseball is a stat driven sport with some sort of analysis occurring on every play.  I decided to research the statistics of this home run ball and analyze the physics behind it.  I was surprised to see the amount of information that exists behind this home run as the exit velocity, launch angle, and distance are recorded.  I found it funny that the hit was referred to as a moonshot, but the height of the home run ball was not listed.  Lucky for me, I already had all of the information needed to find the height.



Launch Angle: 30 degrees
Exit Velocity: 110.5 mph (49.4 m/s)
Distance: 481 feet (146.6 m)
Initial height: waist ≈ 0.9 m

First I had to find the velocity of the y-component through some trigonometry (sin30=opposite/49.4 m/s).  The velocity of the y-component was found to be 24.7 m/s.  At the ball's peak, the velocity of the y-component will be 0 m/s.  With a simple kinematics equation, I was able to find the height of the home run.

vf^2=(vo^2)+2a(yf-yo)→0^2=(24.7^2)+2(-9.8)(yf-0.9)

The height was found to be 32.03 m (105.1 ft). (Ignoring air resistance)
Last year at the baseball game, if someone would have asked me to calculate how high the ball went, I would have had no idea how to do it.  I am proud that it is now just a simple physics problem for me.  I am also very surprised that this stat was not recorded because it is so simple to find.  After preparing this blog post, I am unsure if I will ever be able to watch baseball the same way again.

Source:
https://www.cubshq.com/update/WATCH-Baez-absolutely-destroys-baseball-on-481-foot-moonshot-Cubs-longest-homer-of-season-25398