How high up was the handball launched?

Middle school was a great time; times when we had little responsibilities and when the workload was
a joke- what more can one ask for, right? Recess after lunch was everyone’s most-cherished 45
minutes of their day. Students would run around with a soccer ball in hopes of nutmegging their
fellow friends while others sit and gossip. My friends and I would play pickup basketball, but
oftentimes, we would have to call next while current teams finish up their game. In the meantime,
we would grab a rubber handball and run to opposite ends of the school fence, and throw the
handball to each other. In other words, this was a long-distance version of catch. 

I recall throwing the handball pretty high up, but exactly far far did I launch it? Simple kinematic
could be used to solve this dilemma, despite using a lot of approximations. The distance from
one end of the school fence to the other was approximately 70m. I recall the handball being in
the air for about 3 seconds every time I throw it.

Δx = 70m

t = 3s

Δx = Vot + ½ axt2

70m = Vo(2.5s) + ½ (0m/s2)(2.5s)

Vo = 28m/s

The speed at which I launched the handball was approximately 27m/s- not shabby for an
8th grader. The Vo value is used again for the y-component of the same kinematics formula. 

Δy = Vot + ½ ayt2

Δy = (28m/s)(2.5s) + ½ (9.8m/s2)(2.5s)2

Δy = 100m

100m - 1.8m = 98.2m

The handball was approximately released at a height of 1.8 meters. This means that the
maximum height at which I was able to launch the handball was 98.2 meters above the
ground.