# How Is Distance Calculated in Free Fall with Air Resistance?

• bigjuicy
In summary, free fall with air resistance takes into account the force of air resistance acting on an object, causing the object's speed to decrease and eventually reach a constant terminal velocity. This force is affected by the object's shape, size, and speed. An object can reach a velocity of zero in free fall with air resistance, resulting in a shorter distance traveled compared to regular free fall without air resistance.
bigjuicy
D=Drag Coefficient
p=Density of air
A=Cross sectional area
v=velocity
a=acceleration
F= force

F air=(DpAv^2)/2
F net=mg-F air
ma=mg-F Air
a=g-(DpAv^2)/2m
k=DpA/2m

so
a=g-kv2
dv/dt=g-kv2
dt=dv/g-kv2

using the online integrator from wolfram we got

t=tanh-1(sqrt(k)v/sqrt(g))/sqrt(gk)

we want to solve for distance fallen without t or v in the equation

welcome to pf!

hi bigjuicy! welcome to pf!

(have a square-root: √ )
bigjuicy said:
t=tanh-1(sqrt(k)v/sqrt(g))/sqrt(gk)

we want to solve for distance fallen without t or v in the equation

i'm a little confused as to what you're doing …

you have dz/dt (=v) as a function of t, so solve for z the usual way (but how can you solve for z without t, when distance fallen depends on time? )

## 1. How is free fall with air resistance different from regular free fall?

Free fall with air resistance is different from regular free fall because it takes into account the force of air resistance acting on an object as it falls. In regular free fall, the object is only affected by the force of gravity.

## 2. How does air resistance affect the speed of an object in free fall?

Air resistance causes the speed of an object in free fall to decrease as it falls. This is because air resistance creates a force that opposes the direction of motion, slowing the object down. As the object's speed decreases, the force of air resistance also decreases, until it reaches a point where the force of gravity and the force of air resistance are equal, resulting in a constant terminal velocity.

## 3. What factors affect the amount of air resistance on an object in free fall?

The amount of air resistance on an object in free fall is affected by several factors, including the object's shape, size, and speed. Objects with larger surface areas and higher speeds experience more air resistance, while objects with smaller surface areas and lower speeds experience less air resistance.

## 4. Can an object ever reach a velocity of zero in free fall with air resistance?

Yes, an object can reach a velocity of zero in free fall with air resistance. This occurs when the force of air resistance is equal to the force of gravity, resulting in a constant velocity known as terminal velocity. At this point, the object is no longer accelerating and its velocity remains constant.

## 5. How does the presence of air resistance affect the distance an object travels in free fall?

The presence of air resistance decreases the distance an object travels in free fall. This is because the object's speed decreases due to the opposing force of air resistance, resulting in a shorter distance traveled. In regular free fall, where air resistance is not a factor, the object would travel a greater distance before reaching the ground.

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