# Distance Needed to Reach Terminal Velocity

• elli
In summary, the homework assignment involves solving for the minimum distance needed to reach terminal velocity for an object with a mass of .5kg and a drag coefficient of .6. The solution requires integrating a velocity function from time 0 to 5*time constant, where the time constant is determined by the quadratic drag. The object will reach terminal velocity when the gravitational force and drag force are equal, and the equation for this can be used to find the terminal velocity at any given time.
elli

## Homework Statement

I am completing a homework assignment that involves a python program for air resistance. One of the questions in the assignment asks us to find the minimum distance needed to reach terminal velocity. The air resistance is quadratic. The mass of the object is .5kg and its drag coefficient is .6
The gravity is normal Earth gravity, 9.81m/s^2, and the initial velocity is 0m/s.

## Homework Equations

The force of air resistance=-k*v^2

## The Attempt at a Solution

I think the solution involves integrating a velocity function from time 0 to 5*time constant. However, I'm not sure how to represent the object's velocity under quadratic drag, nor am I sure of the time constant. Is it still m/k, or is it different for quadratic drag?

This is my first post! I appreciate any and all help.

The object will fall with terminal velocity when the gravitational force and the drag force become equal.
ie. mg=k*v^2
Now we know the terminal velocity
At any instant of time
F(net)=mg-kv^2
m.a(net)=mg-kv^2
m.v.(dv/ds)=mg -kv^2 (accn=v. dv/ds)
now integrate the above eqn using proper limits

Thank you very much!

## 1. What is terminal velocity and how is it calculated?

Terminal velocity is the maximum speed that an object will reach when falling through a medium, such as air. It is calculated using the formula v = √(2mg/pAC), where v is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, p is the density of the medium, A is the projected area of the object, and C is the drag coefficient.

## 2. How does distance affect the time it takes to reach terminal velocity?

The distance an object falls can affect the time it takes to reach terminal velocity. The longer the distance, the more time the object has to accelerate. However, once the object reaches terminal velocity, it will no longer accelerate, so the distance will not have an impact on the time it takes to reach terminal velocity.

## 3. What factors influence the distance needed to reach terminal velocity?

The distance needed to reach terminal velocity is influenced by several factors, such as the mass and shape of the object, the density of the medium, and the drag coefficient. Objects with a larger mass or a greater surface area will typically require a longer distance to reach terminal velocity, while objects falling through denser mediums will reach terminal velocity quicker.

## 4. How does air resistance affect the distance needed to reach terminal velocity?

Air resistance, also known as drag, plays a significant role in determining the distance needed to reach terminal velocity. As an object falls, it accelerates due to gravity, but as it gains speed, the force of air resistance increases, eventually balancing out the force of gravity and causing the object to reach terminal velocity. The greater the air resistance, the shorter the distance needed for an object to reach terminal velocity.

## 5. Can the distance needed to reach terminal velocity be affected by external forces?

External forces, such as wind or an external push, can affect the distance needed for an object to reach terminal velocity. These forces can either increase or decrease the amount of time it takes for an object to reach terminal velocity, depending on the direction and magnitude of the force. However, once an object reaches terminal velocity, these external forces will no longer have an impact on its speed.

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