Answer:
The height of the tower is 23.786 m
Explanation:
Given;
period of oscillation, t = 9.79 s
acceleration of gravity, g = 9.8 m/s²
The period of oscillation is calculated as follows;
[tex]t = 2\pi \sqrt{\frac{h}{g} } \\\\[/tex]
where;
h represents the height of the tower
g is the acceleration of gravity
[tex]t = 2\pi \sqrt{\frac{h}{g} } \\\\\sqrt{\frac{h}{g} } = \frac{t}{2\pi} \\\\[/tex]
square both sides of the equation;
[tex](\sqrt{\frac{h}{g} })^2 = (\frac{t}{2\pi} )^2\\\\ \frac{h}{g} = \frac{t^2}{4\pi ^2} \\\\h = \frac{gt^2}{4\pi ^2} \\\\h = \frac{9.8*(9.79)^2}{4\pi ^2}\\\\h = 23.786 \ m[/tex]
Therefore, the height of the tower is 23.786 m
