## A 60 kg Skydiver Moving at Terminal Speed
### Introduction
Skydiving is a thrilling sport that involves jumping out of an airplane and freefalling toward the ground. As the skydiver falls, air resistance acts against them, slowing them down until they reach a constant velocity known as terminal speed. This article will explore the physics behind terminal speed and examine the factors that affect it.
### Terminal Speed
Terminal speed is the maximum velocity that an object can reach when falling through a fluid (such as air or water). It occurs when the force of air resistance is equal to the force of gravity acting on the object. At this velocity, the object’s acceleration is zero.
The equation for terminal speed (v) is:
“`
v = √[(2 m g) / (ρ A Cd)]
“`
where:
m is the mass of the object
g is the acceleration due to gravity
ρ is the density of the fluid
A is the cross-sectional area of the object
Cd is the drag coefficient
### Factors Affecting Terminal Speed
The terminal speed of an object depends on several factors, including:
#### Mass
The greater the mass of an object, the greater its terminal speed. This is because a more massive object has a greater force of gravity acting on it, which requires more air resistance to balance out.
#### Cross-sectional Area
The larger the cross-sectional area of an object, the greater its terminal speed. This is because a larger surface area experiences more air resistance.
#### Drag Coefficient
The drag coefficient is a dimensionless number that quantifies the shape and surface properties of an object. A higher drag coefficient means that the object experiences more air resistance.
#### Air Density
The density of the fluid through which an object is falling affects its terminal speed. Objects falling through denser fluids experience more air resistance and have lower terminal speeds.
### Skydiver at Terminal Speed
A 60 kg skydiver moving at terminal speed experiences the following forces:
Gravity: The force of gravity pulls the skydiver downward with a force of approximately 588 Newtons (60 kg 9.8 m/s^2).
Air Resistance: The resistance of the air acting upward on the skydiver’s body is approximately equal to 588 Newtons at terminal speed.
At this speed, the skydiver’s acceleration is zero, and they continue to fall at a constant velocity of approximately 55 km/h (34 mph).
### Factors Affecting a Skydiver’s Terminal Speed
In addition to the factors discussed above, several specific factors can affect a skydiver’s terminal speed, including:
Body Position: Skydivers can change their body position to increase or decrease their cross-sectional area and drag coefficient. By spreading their limbs, they increase their drag and slow down. By tucking in their limbs, they reduce their drag and accelerate.
Altitude: As a skydiver falls, the air density decreases with increasing altitude. This results in a lower terminal speed at higher altitudes.
Equipment: The weight and aerodynamic properties of a skydiver’s equipment can also affect their terminal speed. Heavier or more streamlined equipment can result in higher or lower terminal speeds, respectively.
### Conclusion
Terminal speed is a crucial concept in understanding the physics of skydiving. It represents the balance between the force of gravity and air resistance and determines the constant velocity that a skydiver reaches during freefall. By understanding the factors that affect terminal speed, skydivers can control their descent and enjoy a safe and exhilarating experience.