Answer: 5.17 m
Explanation:
The football reaches its maximum height when the vertical component of the velocity is zero:
[tex]V_{y}=0 m/s[/tex]
This is exactly at the point where the football stops and then begins to fall thanks to the acceleration due gravity.
So, we can use the following equation:
[tex](V_{y})^{2}=(V_{oy})^{2}-2gy_{max}[/tex]
Where:
[tex]V_{y}=0[/tex] is the final velocity
[tex]V_{oy}=V_{o} sin(32\°)[/tex] is the vertical component of the initial velocity
[tex]V_{o}=19 m/s[/tex] is the initial velocity
[tex]g=9.8 m/s^{2}[/tex] is the acceleration due gravity
[tex]y_{max}[/tex] is the football's maximum height
Isolating [tex]y_{max}[/tex]:
[tex]y_{max}=\frac{(V_{o} sin(32\°))^{2}}{2g}[/tex]
[tex]y_{max}=\frac{(19 m/s sin(32\°))^{2}}{2(9.8 m/s^{2})}[/tex]
Finally:
[tex]y_{max}=5.17 m[/tex] This is the football's maximum height
