The speed of the ball at launch is 23m/s.
After 0.5 seconds, the ball initially passed the pole.
Then it will again reach the top of the pole after 4.1 seconds.
Consequently, the ball's travel time above the pole is
Δt = 4.1 - 0.5 = 3.6sec
Now the time it will take to reach the highest point from the top of the pole is given as t = Δt/2 = 1.8sec.
Now the total time to reach the top from the bottom is given as 2.3sec.
After 0.5 seconds, the ball initially passed the pole.
Consequently, the ball's travel time above the pole is
[tex]v_{f} - v_{i} = at[/tex]
[tex]v_{i}=22.54m/s[/tex]
also the speed after 0.5 s is
[tex]v_{f} = 17.64m/s[/tex]
So, the speed of the ball at launch is 23m/s.
Learn more about speed here;
https://brainly.com/question/93357
#SPJ9