A visitor to a lighthouse wishes to find out the height of the tower. The visitor ties a spool of thread to a small rock to make a simple pendulum. Then, the visitor hangs the pendulum down a spiral staircase in the center of the tower. The period of oscillation is 9.49 s. What is the height of the tower?
The period of a simple pendulum is given by the formula:
T = 2π√(L/g)
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (9.8 m/s^2 approximately).
We can rearrange this formula to solve for L:
L = (gT^2)/(4π^2)
Substituting the given values, we get:
L = (9.8 m/s^2)(9.49 s)^2/(4π^2) = 92.3 m
Therefore, the height of the tower is approximately 92.3 meters.