Theoretical Review Part 2

The acceleration due to gravity is approximately 9.8 meters divided by seconds squared:
g = 9.8m/s²      (1)

At any given time, the velocity of an object moving with gravitational acceleration is (gravitational) acceleration times travel time:

v = gt       (2)

where v is velocity at a given time, and t is time.

This follows from the definiton of acceleration.(a = v/t)

On a Cartesian v-t plane, the movement of an object moving at constant speed would look like this,

Since the area of a rectangle is height times length, which are measured velocity and measured time, the traveled distance is the area of the shaded rectangle.

The movement of an object with a constant acceleration would look like this:

Using the formula for area of a triangle, we can determine that the distance is half of the measured time(base) times the measured velocity(height):

d = 1/2*t1*v1 (3)

Substituting (2) into (3), we get that distance is half of measured time multiplied by acceleration due to gravity multiplied by measured time:

d = 1/2*t1*g*t1

d = 1/2*g*t1^2      (4)

Using this formula, we can determine the height of the building by measuring the time.

To increase accuracy, we must also take into account air resistance and speed of sound.

Note. From formula (4) it follows that the measurement of the height of the building is linearly dependent on acceleration due to gravity. On time, however, it is quadratically dependant. This means that it is more important to know exact time than exact acceleration.