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

• Correct answer
  A

  720 m
• B

  900 m
• C

  320 m
• D

  680 m

Solution

We have $h=\frac{1}{2}{g t^2}^2$ and $h+400=\frac{1}{2} g(t+4)^2$. Subtracting we get $400=8 \mathrm{~g}+4 \mathrm{gt}$ $$ \begin{aligned} & \Rightarrow \mathrm{t}=8 \mathrm{sec} \\ & \therefore \mathrm{h}=\frac{1}{2} \times 10 \times 64=320 \mathrm{~m} \\ & \therefore \text { Desired height }=320+400=720 \mathrm{~m} . \end{aligned} $$

Hence, the correct answer is option: 'A'.