for t (t> 0 )in − 5 t^2 + 30 t= 0 gives t=^6. Substituting t=^6 in
v=− 10 t+ 30
gives − 30 (m/s) of instantaneous velocity when the ball lands.
The moment when the ball reaches its maximum height is when
t= 3 (− 2 ba=−−^3100 = 3 ), so substituting t= 3 in x=− 5 t^2 + 30 t gives
x= 45 m. Substituting t= 3 inv=− 10 t+ 30 gives v= 0 , because at
the top of its flight, the ball is at stationary state, so the velocity always
becomes zero.
// Visualization of Baseball
Representing movements into physical equations and measuring
different velocity is practically very difficult. But MLB has functioned
tracking systems on velocity and angle and measured distances with radar
technologies from the past. Since the 2006 playoffs, PITCHf/x,
developed by Sportvision, has been installed in every stadium.
PITCHf/x is a system using three permanently mounted cameras in the
stadium which tracks the speed and location of a pitched baseball with
an accuracy of better than one mile per hour and one inch. PITCHf/x
analyzes such as the pitcher with the fastest fastball, or the pitcher with
the sharpest-breaking curve, etc. It calculates the "movement" of pitches
including trajectory, speed, spin, break, and location.4 MLB replaced
PITCHf/x with the Trackman system of Statcast in 2017 for official
pitch measurements, but it was still the first technology to provide
specific data of physical movements of pitches in baseball.5 Trackman
could measure values such as extension, spin rate or spin direction in
addition to features of PITCHf/x and new features are getting added
every year.^6