You need to know the height of a tower, but darkness obscures the ceiling. you note that a pendulum extending from the ceiling almost touches the floor and that its period is 28 s. the acceleration of gravity is 9.81 m/s 2 . how tall is the tower?

The height of the tower, where, the pendulum extending from the ceiling almost touches its floor is 195 meters.

Pendulum is the body which is pivoted a point and perform back and forth motion around that point by swinging due to the influence of gravity.

The time period of pendulum is time taken by it to complete one cycle of swing left to right and right to left.

It can be given as,

Here, (g) is the gravitational force of Earth and (L) is the length of the pendulum.

The period of the pendulum is 28 s and the acceleration of gravity is 9.81 m/s². Thus the length of the pendulum is,

As, the pendulum extending from the ceiling almost touches the floor. Thus, the height of the tower, is equal to the length of the pendulum.

Thus, the height of the tower, where, the pendulum extending from the ceiling almost touches its floor is 195 meters.

Learn more about the time period of pendulum here;

link

the approx height of the tower must be 195 m

Explanation:

As we know that time period of simple pendulum is given as

now we know that

now we have

now rearrange the terms to find the value of L

so the approx height of the tower must be 195 m

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)