A body falling under gravity covers two points A and B separated by 80 m in 2 s . The distance of upper…

From $\mathrm{A}\to \mathrm{B}$, using the equation of motion, we have

$$\begin{gathered} -80=-v_{1}t-\frac{1}{2}\times 10t^2 \\ \Rightarrow -80=-2v_1-\frac{1}{2}\times 10\times 2^2 \\ \Rightarrow -80=-2v_1-20 \\ \Rightarrow -60=-2v_1 \\ \Rightarrow v_1=30 \mathrm{m} {\mathrm{s}}^{-1} \end{gathered}$$$$

From $\mathrm{O}$ to $\mathrm{A}$, it follows that

$$\begin{gathered} v^2=u^2+2gS \\ \Rightarrow {30}^2=0+2\times (-10)(-S) \\ \Rightarrow 900=20 S \\ \Rightarrow S=45 \mathrm{m} \end{gathered}$$