what distance does the top of the empire state building travel horizantally
To calculate the horizontal distance traveled by the top of the Empire State Building, we'll need to know the height of the building and the angle at which it leans or sways.
If we assume that the Empire State Building is not leaning or swaying, we can use basic trigonometry to determine the horizontal distance traveled. Here's how:
1. Find the height of the Empire State Building. According to the official website, the height of the building from its base to the tip of the lightning rod is 1,454 feet, or approximately 443.2 meters.
2. Determine the angle of the top of the building. This angle can vary depending on factors such as wind speeds and building design. As an estimate, let's assume that the top of the building sways about 1 degree from the vertical at its maximum displacement.
3. Calculate the horizontal distance traveled. Using trigonometry, we can use the height and the angle to find the horizontal distance. The formula is: horizontal distance = height * tangent(angle).
In this case, the angle needs to be in radians, so we need to convert it from degrees. The formula to convert degrees to radians is: angle in radians = angle in degrees * π / 180.
Let's calculate the horizontal distance traveled using these values:
Height = 443.2 meters
Angle (in radians) = 1 degree * π / 180 ≈ 0.01745 radians
Horizontal distance = 443.2 meters * tangent(0.01745 radians)
Using a scientific calculator, the tangent of 0.01745 radians is approximately 0.000305 radians.
Horizontal distance ≈ 443.2 meters * 0.000305 ≈ 0.135 meters.
Therefore, the top of the Empire State Building would travel approximately 0.135 meters horizontally when it sways 1 degree from the vertical.