What Is The Terminal Velocity Of A Falling Human

Have you ever wondered what happens when a person falls from a great height? While it's not a pleasant thought, understanding the physics behind falling objects, including humans, is crucial in various fields, such as physics, engineering, and even skydiving. One important concept to grasp is terminal velocity, which is the maximum speed an object can reach as it falls through a fluid, like air. In this article, we'll delve into the terminal velocity of a falling human and explore the factors that influence it.

Understanding Terminal Velocity

When an object falls, it initially accelerates downward due to gravity. However, as it gains speed, air resistance, also known as drag, starts to slow it down. As the object continues to fall, the force of gravity pulling it downward is balanced by the force of drag pushing it upward. At this point, the object reaches its terminal velocity, where its speed remains constant.

Factors Affecting Terminal Velocity

Several factors influence the terminal velocity of a falling human:

Mass: The more massive the object, the higher its terminal velocity. A heavier person will generally reach a higher terminal velocity than a lighter one.
Shape and size: The shape and size of the object affect the amount of air resistance it encounters. A larger surface area or a more streamlined shape can reduce air resistance and increase terminal velocity.
Air density: The density of the air affects the amount of drag an object experiences. Thicker air, like at lower altitudes, provides more resistance than thinner air, like at higher altitudes.
Altitude: As altitude increases, air density decreases, which reduces air resistance and allows objects to reach higher terminal velocities.
Orientation: The orientation of the object during free fall also affects its terminal velocity. A person in a head-down position, also known as a " belly-to-earth" position, will generally reach a higher terminal velocity than one in a head-up position.

Calculating Terminal Velocity

To calculate the terminal velocity of a falling human, we can use the following formula:

v_t = √(2 * m * g / (ρ * A * C_d))

where:

v_t = terminal velocity (m/s)
m = mass of the person (kg)
g = acceleration due to gravity (m/s^2)
ρ = air density (kg/m^3)
A = cross-sectional area of the person (m^2)
C_d = drag coefficient (unitless)

Estimating Terminal Velocity

Estimating the terminal velocity of a falling human is a complex task, as it depends on various factors, including the person's mass, shape, size, and orientation. However, we can make an educated estimate based on average values.

Assuming a person with a mass of around 70 kg (154 lbs) and a cross-sectional area of about 0.1 m^2 (1.08 ft^2), we can estimate the terminal velocity as follows:

v_t ≈ √(2 * 70 kg * 9.8 m/s^2 / (1.2 kg/m^3 * 0.1 m^2 * 0.47)) ≈ 53 m/s (117 mph)

This is a rough estimate and can vary depending on the specific conditions.

Real-World Examples

To put these calculations into perspective, let's look at some real-world examples:

Skydivers can reach terminal velocities of up to 120-140 mph (193-225 kph) during free fall, depending on their body position and the altitude at which they jump.
BASE jumpers, who jump from fixed structures like buildings or bridges, can reach terminal velocities of up to 100-120 mph (161-193 kph).
A person falling from a great height, like a skyscraper or a cliff, may reach a terminal velocity of around 50-70 mph (80-113 kph), depending on their body position and the air density.

Conclusion

In conclusion, the terminal velocity of a falling human is a complex phenomenon influenced by various factors, including mass, shape, size, air density, altitude, and orientation. While estimating terminal velocity can be challenging, understanding the underlying physics is essential in fields like physics, engineering, and skydiving. Whether you're a thrill-seeker or simply curious about the world around you, grasping the concept of terminal velocity can help you appreciate the intricacies of our physical world.

Gallery of Falling Objects