Given data:
Initial velocity,
[tex]u=20\text{ m/s}[/tex]Angle of projection,
[tex]\theta=22\degree[/tex]The maximum height achieved by the projectile is given as,
[tex]H=\frac{u^2\sin ^2\theta}{2g}[/tex]Here, g is the acceleration due to gravity.
Substituting all known values,
[tex]\begin{gathered} H=\frac{(20\text{ m/s})^2\times\sin ^2(22\degree)}{2\times(9.8\text{ m/s}^2)} \\ \approx2.86\text{ m} \end{gathered}[/tex]Therefore, the maximum height achieved by the projectile is 2.86 m.
