## A 70 kg Skydiver Falling at Terminal Speed
When a skydiver jumps out of an airplane, they accelerate due to the force of gravity. The air around the skydiver also exerts a force on them, called air resistance. As the skydiver falls, the air resistance increases until it reaches a point where it is equal to the force of gravity. At this point, the skydiver reaches their terminal speed.
The terminal speed of a skydiver depends on a number of factors, including their weight, surface area, and the density of the air. For a 70 kg skydiver, the terminal speed is approximately 195 km/h.
### The Forces Acting on a Skydiver
There are four main forces acting on a skydiver:
Gravity: The force of gravity is the force that pulls the skydiver towards the ground. The force of gravity is proportional to the skydiver’s mass.
Air resistance: The force of air resistance is the force that opposes the skydiver’s motion through the air. The force of air resistance is proportional to the skydiver’s velocity and the density of the air.
Buoyancy: The force of buoyancy is the force that opposes the skydiver’s weight due to the air pressure. The force of buoyancy is proportional to the volume of the skydiver’s body and the density of the air.
Lift: The force of lift is the force that opposes the skydiver’s weight due to the shape of their body. The force of lift is proportional to the skydiver’s velocity and the density of the air.
### The Skydiver’s Terminal Velocity
The skydiver’s terminal velocity is the velocity at which the force of gravity is equal to the force of air resistance. At terminal velocity, the skydiver is no longer accelerating and is falling at a constant speed.
The terminal velocity of a skydiver can be calculated using the following equation:
“`
v = √(2mg/ρACd)
“`
where:
v is the terminal velocity
m is the mass of the skydiver
g is the acceleration due to gravity
ρ is the density of the air
A is the surface area of the skydiver
Cd is the drag coefficient
For a 70 kg skydiver, the terminal velocity is approximately 195 km/h.
### The Effects of Terminal Velocity
The terminal velocity of a skydiver has a number of effects, including:
The skydiver’s rate of fall: The skydiver’s rate of fall is equal to their terminal velocity. This means that the skydiver will fall at a constant speed until they reach the ground.
The skydiver’s impact force: The skydiver’s impact force is the force that they exert on the ground when they land. The impact force is proportional to the skydiver’s velocity and mass. At terminal velocity, the skydiver’s impact force is much greater than it would be if they were falling at a slower speed.
The skydiver’s risk of injury: The skydiver’s risk of injury is greater at terminal velocity than it would be if they were falling at a slower speed. This is because the impact force is greater at terminal velocity.
### Conclusion
The terminal velocity of a skydiver is a critical factor to consider when planning a skydive. By understanding the factors that affect terminal velocity, skydivers can minimize their risk of injury and enjoy a safe and exciting skydiving experience.