The maximum height is 16.8 m
In order to find the maximum height reached by the football, we can just analyze its vertical motion.
The vertical motion of the ball is a free fall motion, affected only by the force of gravity. So it is a uniformly accelerated motion, and we can use suvat equations.
First of all, we notice that the motion of the ball is symmetrical, so the time taken to reach the maximum height is equal to the time needed to fall down: Since the total time of flight is
T = 3.7 s
It means that the time to reach the maximum height is
We can now find the maximum height reached using the equation:
s is the vertical displacement (the maximum height)
v = 0 is the velocity of the ball at the maximum height
t = 1.85 s is the time
is the acceleration of gravity
Solving for s,
Learn more about free fall motion here: