Answer to Question #280506 in Physics for Faith

Question

Juan wants to know the height of a museum. Inside the museum, he notices a very long simple pendulum extending from the ceiling and almost touching the floor. Remembering his lessons in physics, he realizes that he can estimate the height of the museum from the period of the pendulum’s oscillation. If the pendulum undergoes one complete oscillation in 22.99 seconds, how tall is the tower?

Answer 1

$$T=2\pi\sqrt{\dfrac{l}{g}},$$ $$T^2=4\pi^2\dfrac{l}{g},$$ $$h=l=\dfrac{T^2g}{4\pi^2}=\dfrac{(22.99\ s)^2\times9.8\ \dfrac{m}{s^2}}{4\pi^2}=131.2\ m.$$