Uniform Free Fall

Unifrom Free Fall in 2D

Below is a simulation of uniform free fall. It differs from the simulations following it in that it does not consider air resistance, the drag coefficient, cross-sectional area of the object, or the bounce index of the object when it hits the ground. Here we only consider the gravity of the object, and the initial velocity of the object when it is dropped from an arbitrary height chosen by you. Once the ball will fall, a final velocity of the object will be calculated along with the time of flight.

Initial Velocity:
Gravity:

What is uniform free fall? Uniform free fall takes a loom at a falling object at a given height not considering the drag force coefficient, air resistance, cross-sectional area of the object, or the bounce index of the object when it hits the ground. These additional variables will be further discussed in Non-uniform free fall. Uniform free fall looks at a falling object in an ideal world scenario. To calculate the time of how long the object traveled, the displacement kinematic equation can be used. Since the final height will be 0, and the initial height will be chosen by you, those are given. You also decide what to input for the acceleration due to gravity and the initial velocity, so what is left to be determined is the time of flight of the falling object. Once you determine how long the object traveled you can solve for the terminal velocity of the object using the final velocity kinematic equation.

These formulas work for an object dropping from any height, starting at any initial velocity, and falling from any acceleration due to gravity. These formulas work because again this is uniform free fall, meaning that this works in the case of an ideal free fall of an object without factoring additional factors mentioned above, which will be further discussed in non-uniform free fall.

Here is the original kinematic equation to solve for an object's displacement:

\[ \Delta x = x_f - x_i = v_i t - \frac{1}{2} a t^2 \]

\[ x_f = x_i + v_i t - \frac{1}{2} a t^2 \]

Here is how the displacement kinematic equation is adjusted for free fall:

\[ y_f = y_i + v_i t + \frac{1}{2} g t^2 \]

y represents the displacement of the object along the y-axis since the object is going from up down, not left to right.

g represents the acceleration due to gravity not regular acceleration like a.

+ replaces - because acceleration due to gravity is negative and for the formula to work properly, this change is introduced.

Here is a sample use of the displacement equation, which you can check yourself, using the simulation:

\[ y_f = y_i + v_i t + \frac{1}{2} g t^2 \]

\[ 0 = (40) + (0) t + \frac{1}{2} (-9.81) t^2 \]

\[ 0 = 40 + 0 - 4.905 t^2 \]

\[ -40 = -4.905 t^2 \]

\[ \frac{-40}{-4.905} = \frac{-4.905 t^2}{-4.905} \]

\[ 8.1549439 = t^2 \]

\[ \sqrt{8.1549439} = \sqrt{t^2} \]

\[ 2.85556862 \approx t \]

\[ 2.9 \text{s} \approx t \]

\[ t \approx 2.9 \text{s} \]

Here is the original kinematic equation to solve for the object's final velocity:

\[ v_f = v_i - a t \]

Here is how the displacement kinematic equation is adjusted for free fall:

\[ v_f = v_i - g t \]

g represents the acceleration due to gravity not regular acceleration like a.

Here is a sample use of the final velocity equation, which you can check yourself, using the simulation:

\[ v_f = v_i - g t \]

\[ v_f = 0 - (-9.81) (2.9) \]

\[ v_f = 0 - (-28.449) \]

\[ v_f = 0 + 28.449 \]

\[ v_f = 28.449 \]

\[ v_f = 28 \text{m/s} \]

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