In case of free fall displacement of the motion
\(S = \frac 12 gt^2\)
nth four second
(n - 5)th = tn-5
given (tn - tn-5) = 5
Displacement in last five second
\(S_{n , n-5} = \frac 12 g (t_n - t_{n -5})^2\)
\(200 = \frac 12 \times 10\times (t_n - t_{n - 5})^2\)
\(40 = (t_n - t_{n - 5}) (t_n + t_{n - 5})\)
\(40 = 5 (t_n + t_{n - 5})\)
\(8 = t_n + t_{n - 5}\)
Solving equation (1) and (2)
\(\begin{array}{r}t_n + t_{n-5} = 8\\t_n - t_{n - 5} = 5\\\hline 2t_n
= 13\end{array}\)
\(t_n = \frac{13}2\)
\(t_n = 6.5 \) sec
\(t_{n-5} = 5 + 6.5\)
\(t_{n-5} = 11.5\)
Height of the building
\(S = \frac 12 gt^2\)
\(S = \frac 12 \times 10\times (6.5)^2\)
\(S = 5\times 42.25\)
\(S = 211.25\)
