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  4. A body falling freely under gravity passes two points 30 m apart in 1 s. From what point above the upper point it began to fall? (Take g= 9.8 m s-2).

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Q. A body falling freely under gravity passes two points $30\, m$ apart in $1 \,s$. From what point above the upper point it began to fall? (Take $g= 9.8 \,m \,s^{-2}$).

Motion in a Straight Line

Solution:

Suppose the body passes the upper point at $t$ second and lower point at $(t + 1)\, s$, then
$S_{2}-S_{1}=\frac{1}{2}g\left(t+1\right)^{2}-\frac{1}{2}gt^{2}$
$=\frac{1}{2} g\left(2t+1\right)$
or $30\,m=\frac{1}{2}\times9.8\left(2t+1\right)$
$\therefore t=2.56\,s$
$S_{1}=\frac{1}{2} \,gt^{2}=\frac{1}{2} \times9.8\times\left(2.56\right)^{2}$
$=32.1\,m$