A stone dropped from top of tower is found to travel (5/9) of the height of tower during the last - Physics - Motion In A Straight Line

Question

A stone dropped from top of tower is found to travel (5/9) of
the height of tower during the last second of its fall The time of
fall is??

Himanshu · Accepted Answer

Let the time of fall be n seconds Let the height of the tower be h m Therefore, $h = \frac{1}{2} g n^{2}$ Also, $\frac{5 h}{9} = \frac{1}{2} g n^{2} - \frac{1}{2} g (n - 1)^{2} \Rightarrow \frac{5 h}{9} = \frac{1}{2} g (2 n - 1) \Rightarrow \frac{5}{9} (\frac{1}{2} g n^{2}) = \frac{1}{2} g (2 n - 1) \Rightarrow 5 n^{2} - 18 n + 9 = 0 \Rightarrow 5 n^{2} - 15 n - 3 n + 9 = 0 \Rightarrow (n - 3) (5 n - 3) = 0 n = 3$

A stone dropped from top of tower is found to travel (5/9) of the height of tower during the last second of its fall. The time of fall is??