Here are some of the basic equations for falling/dropping objects. The variables use the metric system, click here for the default values. The variables are for a human male, falling on the planet Earth. The "Other" list values are for the planet Earth, which uses it's equatorial radius.

- Falling (without air resistance) using distance
- Sqrt(2*d /g) = time until impact dropped (x) distance seconds
- Sqrt(2*d*g) = velocity on impact after (x) distance m/s

- Air resistance
- ρ*A*Cd = (k) air resistance coefficient dimensionless
- 0.5*v^2*k = drag force or air resistance Newtons
- Sqrt((2*m*g)/k) = terminal velocity m/s

- Falling (with air resistance) using distance
- Sqrt(m/(g*k))*ArcCosh(e^d*k/m)) = time elapsed after falling (x) distance seconds

- Falling (with air resistance) using time
- Sqrt(m*g/k)*Sqrt(m/(g*k))*Log(Cosh(t/Sqrt(m/(g*k)))) = distance fallen after (x) time meters
- Sqrt(m*g/k)*Tanh(t/Sqrt(m/(g*k))) = velocity after (x) time m/s

- Other
- m * g = weight Newtons
- mass of planet * gravitational constant / radius of planet ^ 2 = gravitional acceleration m/s^2

- (d) distance dropped
- (g) gravitational acceleration
- (m) mass of falling object

- (ρ) density of fluid
- (A) frontal area
- (Cd) drag coefficient

- (v) current velocity
- (t) time in free-fall

- mass of planet
- radius of planet
- gravitational constant

- 2.71828182845905 (e) natural logarithm

More free fall calculators at keisan.casio.com.

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Mass (kilograms)

Frontal Area (meters)

Drag Coefficient

Distance (meters)

Air Density (kg/m^3)

Gravitational Acc. (m/s)

Elasticity of Collision

Falling object

Environment

Falling Distance

Elasticity of Collision

Mass (pounds)

Distance (feet)

Seconds:

Simulation Seconds:

Calculations:

Distance (feet):

Terminal Vel. (m/s):

Velocity (m/s):

Velocity (mph):

Weight (N):

Air Resistance (N):

Net Force (N):

Acceleration (m/s/s):

Energy (j):

KE (j):

GPE (j):

Settings:

Mass (kg):

Frontal Area (m):

Drag Coefficient

Distance (m):

Air Density:

Gravitational Accel. (m/s/s):

Elasticity of Collision:

Delta Time:

Meters Per Pixel:

Integration Method:

**FORCE:** Notice how terminal velocity is reached once the weight in Newtons is equal to air resistance in Newtons. Once the downward force (weight), and the upward force (air resistance) are equal, there is no more acceleration. Without air resistance (the upward force), acceleration would continue since the upward force of air resistance would remain at zero in a vacuum.

**ATTENTION!** This simulation can give you an a basic sense of how fast something will fall, it is not extremely precise. Don't try to use this in Internet Explorer, it seems to be too slow and innaccurate. Mozilla Firefox and Apple Safari work fine, the standalone .NET version works fine as well.
Also, the .NET version is a little more advanced, it has collision detection and elasticity of collision.