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Free Fall Calculator

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This calculator allows you to solve various aspects of free fall motion due to gravity. You can calculate unknown variables like:

  • Time it takes for an object to fall
  • Final velocity before impact
  • Height from which the object fell
  • Initial velocity of the object (if thrown up or down)

How to Use This Calculator

  1. Use the dropdown menu to choose which variable you want to solve for.
  2. Input values for the known quantities (e.g., time, height, initial velocity).
  3. The calculator will compute the desired result based on the laws of motion.

Formulas Used

This calculator uses 9.80665 m/s2 as the default gravitational acceleration. It is the standard gravity value on Earth at sea level and at a latitude of 45 degrees.

Note that 9.80665 m/s2 is equal to 1 g.

Free fall formulas are defined using these five variables:

  • t = Time (seconds)
  • vi = Initial velocity (m/s)
  • vf = Final velocity (m/s)
  • g = Acceleration due to gravity (m/s2)
  • h = Height (m)

1. Time of Fall

If an object falls from rest or with a known initial velocity, the time to fall a known height can be found using:

t=vf−vigt=\frac{v_f-v_i}{g}

Or, if initial velocity is known and height is given:

t=−vi+vi2+2ghgt=\frac{-v_i+\sqrt{v_i^2+2gh}}{g}

2. Final Velocity

The velocity of an object in free fall after a certain time or from a certain height can be calculated as:

vf=vi+gtv_f=v_i+gt

Or, when falling from rest (vi = 0):

vf=2ghv_f=\sqrt{2gh}

3. Height (Displacement)

The distance an object falls in free fall can be calculated using:

h=vit+12gt2h=v_it+\frac{1}{2}gt^2

Or from the final velocity:

h=vf2−vi22gh=\frac{v_f^2-v_i^2}{2g}

4. Initial Velocity

If the final velocity and time are known, initial velocity is:

vi=vf−gtv_i=v_f-gt

Or from displacement and time:

vi=h−12gt2tv_i=\frac{h-\frac{1}{2}gt^2}{t}

Understanding Free Fall

Free fall describes the motion of an object under the sole influence of gravity, with no air resistance. All objects, regardless of mass, accelerate downward at approximately 9.81 m/s2 near Earth's surface.

If an object is dropped from rest, it accelerates continuously, increasing its speed until it hits the ground. If it's thrown upward or downward, initial velocity must be accounted for.

Applications of Free Fall Calculations

Free fall calculations are fundamental in many areas of physics and engineering. Practical applications include:

  • Estimating impact speeds and fall durations in safety engineering
  • Analyzing motion in sports science and biomechanics
  • Calculating trajectories in aerospace and ballistics
  • Modeling vertical motion in amusement park rides and drones

This calculator helps reinforce concepts of gravity, acceleration, and motion while providing real-world problem-solving tools.