The Empire State Building in New York City stands at a height of approximately 1,454 feet (443.2 meters) from its base to the tip of its antenna. If we assume that air resistance is negligible, we can use basic physics equations to estimate how far a penny would fall from the top to street level.
The distance fallen by an object in free fall can be calculated using the formula:
d = (1/2) * g * t^2
where: d = distance fallen g = acceleration due to gravity (approximately 9.8 m/s^2) t = time of fall
To find the time it takes for the penny to fall, we can use the equation:
d = (1/2) * g * t^2
Rearranging the equation, we get:
t = sqrt((2 * d) / g)
Now, let's calculate the time it takes for the penny to fall from the top of the Empire State Building:
d = 443.2 meters g = 9.8 m/s^2
t = sqrt((2 * 443.2) / 9.8) t ≈ sqrt(90.163) ≈ 9.5 seconds (rounded to one decimal place)
So, it would take approximately 9.5 seconds for the penny to reach street level when dropped from the top of the Empire State Building.
To calculate the distance fallen, we can substitute the value of time back into the equation:
d = (1/2) * g * t^2 d = (1/2) * 9.8 * (9.5^2) d ≈ 441.2 meters (rounded to one decimal place)
Therefore, the penny would fall approximately 441.2 meters (or 1,448 feet) from the top of the Empire State Building to reach street level.