A body falling freely under gravity passes two points 30 m apart in 1s. From what point above the upper point it began to fall? (Take g = 10 ms ^-2)

Suppose the body passes the upper point at t second and lower point at (t + 1) s, then

${\mathrm{S}}_2-{\mathrm{S}}_1=\frac{1}{2}\mathrm{g}(\mathrm{t}+1{)}^2-\frac{1}{2}{\mathrm{gt}}^2=\frac{1}{2} g(2t + 1)$

or $30\mathrm{m}=\frac{1}{2}\times 10(2\mathrm{t}+1)$

$\begin{array}{l}\therefore \mathrm{t}=2.5\mathrm{s}\\ {\mathrm{S}}_1=\frac{1}{2}{\mathrm{gt}}^2=\frac{1}{2}\times 10\times (2.5{)}^2=31\\ .25\mathrm{m}\end{array}$