Answer:
Height of tower equals 122.5 meters.
Explanation:
Since the height of the tower is 'H' the total time of fall of stone 't' is calculated using second equation of kinematics as
Since the distance covered in last 1 second is [tex]\frac{9H}{25}[/tex] and the total distance covered in 't' seconds is 'H' thus the distance covered in the first (t-1) seconds of the motion equals
[tex]S_{t-1}=S_{t}-S_{last}\\\\S_{t-1}=H-\frac{9H}{25}=\frac{16H}{25}[/tex]
Now by second equation of kinematics we have
[tex]S=ut+\frac{1}{2}gt^{2}\\\\S=\frac{1}{2}gt^{2}(\because u=0)[/tex]
Thus we have
[tex]\frac{16H}{25}=\frac{1}{2}g(t-1)^{2}.............(i)\\\\H=\frac{1}{2}gt^{2}..............(ii)[/tex]
Dividing i by ii we get
[tex]\frac{16}{25}=\frac{(t-1)^{2}}{t^2}\\\\\therefore \frac{t-1}{t}=\frac{4}{5}\\\\\therefore t=5secs[/tex]
Thus from equation ii we obtain 'H' as
[tex]H=\frac{1}{2}\times 9.8\times 5^{2}=122.5meters[/tex]
