A ball thrown vertically upwards with a speed of 20 m s −...

Let the height of the tower be h. Assume that things are moving in the right direction.
The height of the tower determines the displacement's size. Compared to the initial position, the final position (ground) is downward (or negative).
$\therefore s=-h$
Acceleration is in downwards direction.
$\therefore a=-g=-10m{s}^{-2}$
From the second equation of motion,
$$\begin{gathered} s=ut+\frac{1}{2}a{t}^2 \\ \Rightarrow -h=ut-\frac{1}{2}g{t}^2 \\ \Rightarrow -h=20\times 8-(\frac{1}{2}\times 10\times 8^2) \\ \Rightarrow h=160m \end{gathered}$$