Free Fall with Air Resistance Calculator
Calculate velocity and position of a falling object considering linear air resistance. Enter object mass, drag coefficient, and time of fall.
What this calculator is doing
This calculator estimates the velocity and displacement of a falling object under gravity with **linear air resistance**, where the drag force is proportional to velocity:
\[ F_{\text{drag}} = -kv \]
The governing differential equation: \[ m \frac{dv}{dt} = mg - kv \]
Solving this gives:
Velocity at time \( t \): \[ v(t) = \frac{mg}{k} \left(1 - e^{-\frac{k}{m}t} \right) \]
Displacement from initial position: \[ y(t) = \frac{mg}{k}t - \frac{m^2g}{k^2} \left(1 - e^{-\frac{k}{m}t} \right) \]
Where:
\( m \) = mass of object (kg)
\( g \) = gravitational acceleration (9.81 m/s²)
\( k \) = drag coefficient (kg/s)
\( t \) = time (s)
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