A body freely falling from a height h describes $\frac{7\mathrm{h}}{16}$in the last second of its fall. The height h is (g = 10 ms^–2)

$\begin{array}{l}{\mathrm{S}}_{\mathrm{n}}=\mathrm{u}+\frac{1}{2}\mathrm{g}(2\mathrm{n}-1)\Rightarrow \frac{7\mathrm{h}}{16}=\frac{1}{2}\mathrm{g}(2\mathrm{n}-1)\\ \text{But }\mathrm{h}=\frac{1}{2}{\mathrm{gt}}^2=\frac{1}{2}{\mathrm{gn}}^2\\ \therefore \frac{7}{16}\times \frac{1}{2}{\mathrm{gn}}^2=\frac{1}{2}\mathrm{g}(2\mathrm{n}-1)\\ 7{\mathrm{n}}^2=32\mathrm{n}-16\\ 7{\mathrm{n}}^2-32\mathrm{n}+16=0\therefore \mathrm{n}=4\\ \therefore \mathrm{h}=\frac{1}{2}{\mathrm{gn}}^2=\frac{1}{2}\times 10\times 4^2=\frac{10\times 16}{2}=80\mathrm{m}\end{array}$