Question

A visitor to a lighthouse wishes to determine the height of the tower. She ties a spool of thread to a small rock to make a simple pendulum, which she hangs down the center of a spiral staircase of the tower. The period of oscillation is 9.79 s. The acceleration of gravity is 9.8 m/s 2 . What is the height of the tower

Answer 1

The height of the tower is 23.786 m

Step-by-step 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;

`t = 2\pi \sqrt{(h)/(g) } \\\\`

where;

h represents the height of the tower

g is the acceleration of gravity

`t = 2\pi \sqrt{(h)/(g) } \\\\\sqrt{(h)/(g) } = (t)/(2\pi) \\\\`

square both sides of the equation;

`(\sqrt{(h)/(g) })^2 = ((t)/(2\pi) )^2\\\\ (h)/(g) = (t^2)/(4\pi ^2) \\\\h = (gt^2)/(4\pi ^2) \\\\h = (9.8*(9.79)^2)/(4\pi ^2)\\\\h = 23.786 \ m`

Therefore, the height of the tower is 23.786 m