A body falling from rest under gravity passes a certain point P.

Question

A body falling from rest under gravity passes a certain point $P$. It was at a distance of 400 m from $P$, 4 s prior to passing through $P$. If $g=10\,	ext{m/s}^2$, then the height above the point $P$ from where the body began to fall is:

Accepted Answer

Let the fall time to $P$ be $t$: $h=\dfrac12gt^2$ and $h+400=\dfrac12g(t+4)^2$. Subtracting: $400=8g+4gt \implies t=8\text{ s}$

$$h=\frac12(10)(64)=320\text{ m} \implies \text{required height}=320+400=720\text{ m}$$

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