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 6.01 s. What is the height of the tower

Answer 1

The height of the tower is 8.96 m.

Step-by-step explanation:

We have, 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 6.01 s.

It is required to find the height of the tower. Let it is l. The time period of a simple pendulum is given by :

`T=2\pi \sqrt{(l)/(g)}`

l is length of pendulum, or height of tower

`l=(T^2g)/(4\pi^2)\\\\l=((6.01)^2* 9.8)/(4\pi^2)\\\\l=8.96\ m`

So, the height of the tower is 8.96 m.