The Physics of Falling from the Empire State Building: A King Kong Riddle

Oh, my dear reader, if you expected to learn about the thrilling descent of King Kong from the Empire State Building, then my apologies for ruining your fantasy. King Kong, a beloved fictional character, never actually scaled or fell from this iconic New York skyscraper. However, let's take a step into the world of physics and mathematics to understand the true physics involved in such a notorious fall.

Care to Do the Math?

For those who, like me, find joy in mathematical exercises, let's dive in. We know the height of the Empire State Building is 360 meters, and we can use physics principles to determine how long it would take for an object to fall from this height. To simplify, let's consider the object to be King Kong, a human-sized character, and assume no air resistance. Ready to put on your thinking caps?

Basic Physics Equation

The time it takes for an object to fall freely can be determined using the following equation:

t √(2h/g)

Where:

t time in seconds h height in meters g acceleration due to gravity, approximately 9.8 m/s2 on Earth

Using this equation, we can calculate the time it would take for King Kong to fall straight from the Empire State Building.

Calculating the Fall Time

Let's plug in the numbers:

t √((2 * 360) / 9.8)

t √(720 / 9.8)

t √(73.469)

t ≈ 8.57 seconds

Therefore, it would take approximately 8.57 seconds for King Kong to fall straight from the Empire State Building, assuming no air resistance or other external factors affecting the fall.

Exploring Terminal Velocity

But what about terminal velocity? At terminal velocity, the force of gravity is balanced by the resistance of the air. For an object with a body mass similar to a human, the terminal velocity is around 53 m/s (190 km/h). Let's see how long it would take to reach terminal velocity and how much distance remains to be covered.

First, we need to calculate the time to reach terminal velocity:

v √(2gh)

53 √(2 * 9.8 * h)

(53)2 2 * 9.8 * h

2809 19.6 * h

h ≈ 143.1 meters

Now, we can calculate the remaining distance:

Remaining distance 360 - 143.1 216.9 meters

Let's calculate the time to cover this remaining distance at terminal velocity:

Time Distance / Speed

Time 216.9 / 53 ≈ 4.08 seconds

In total, it would take King Kong approximately 8.57 seconds to fall with no air resistance, and an additional 4.08 seconds to cover the remaining distance at terminal velocity. In real life, air resistance would play a significant role, greatly increasing the time and distance.

Thus, we have delved into the physics of a mythological fall, revealing the surprising simplicity and complexity of the calculations involved. Whether in fiction or reality, King Kong would take a bit longer than just a few seconds to reach the ground from the Empire State Building.