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Free Fall Calculator

Calculate impact velocity, time of fall, and motion under constant gravitational acceleration

Parameters

mⓘ
m/sⓘ
Show Trail

Controls

xⓘ

Calculated Values

Impact Velocity:
31.32;m/s31.32;m/s
Time of Fall:
3.19;s3.19;s
Average Velocity:
15.66;m/s15.66;m/s
Gravitational Acceleration:
9.81;m/s29.81;m/s²

Examples

Ball from 45 m

Object dropped from 45 m (v₀ = 0).

  • Impact Velocity: 29.7129.71
  • Time of Fall: 3.033.03

Thrown downward

5 m/s initial downward velocity from 20 m.

  • Impact Velocity: 20.9020.90
  • Time of Fall: 1.621.62

Visualization

What Is Free Fall?

Free fall is motion when gravity is the only significant force. With air resistance neglected, every object near Earth's surface accelerates downward at g ≈ 9.81 m/s² regardless of mass—Galileo's principle, verified on the Moon.

Constant acceleration means SUVAT applies with a = g (downward positive). Velocity grows linearly: v = v₀ + gt. Displacement grows quadratically: h = v₀t + ½gt².

The velocity–displacement relation v² = v₀² + 2gh finds impact speed without time. From rest: v = √(2gh) and t = √(2h/g). Doubling height increases speed by √2, not 2.

With initial downward speed v₀ > 0, solve the quadratic h = v₀t + ½gt² for t (positive root). Energy conservation gives the same impact speed when only gravity does work.

Real motion includes air drag and terminal velocity; short classroom drops are well modeled with constant g.

Key Concepts

  • g ≈ 9.81 m/s²: gravitational acceleration near Earth's surface
  • v = v₀ + gt: velocity increases linearly with time
  • h = v₀t + ½gt²: displacement (quadratic in t)
  • v² = v₀² + 2gh: links speed and height without time
  • From rest: v = √(2gh), t = √(2h/g)
  • Mass-independent in vacuum; drag matters in air

Real-World Applications

  • Class 9-12 exams: stones from towers
  • Lab measurement of g
  • Skymotion and parachutes
  • Safety: impact speed from height
  • Moon: use g = 1.62 m/s^2

Explore Further

More mechanics tools

Physics Equations

Impact Velocity:
v=v02+2ghv = \sqrt{v_0^2 + 2gh}
Time of Fall:
h=v0t+12gt2h = v_0 t + \frac{1}{2}gt^2
Average Velocity:
vavg=htv_{avg} = \frac{h}{t}

Step-by-Step Solution

See how the main results are calculated.

1

Identify Given Quantities

List known values and choose downward as the positive direction (standard for free-fall problems).

Equation:

g=9.81 m/s2,h=drop height,v0=initial speedg = 9.81 \text{ m/s}^2, \quad h = \text{drop height}, \quad v_0 = \text{initial speed}

Calculation:

h=50 m,v0=0 m/s,g=9.81 m/s2h = 50 \text{ m}, \quad v_0 = 0 \text{ m/s}, \quad g = 9.81 \text{ m/s}^2

Result:

Ready to apply constant-acceleration kinematics

Explanation:

Free fall means the only force is gravity (air resistance neglected). Acceleration is constant at g downward.

2

Calculate Impact Velocity

Use the velocity–displacement equation (no time required):

Equation:

v2=v02+2ghv^2 = v_0^2 + 2gh

Calculation:

v2=(0)2+2(9.81)(50)v^2 = (0)^2 + 2(9.81)(50)
v2=981.00v^2 = 981.00
v=981.00=31.32 m/sv = \sqrt{981.00} = 31.32 \text{ m/s}

Result:

v=31.32 m/sv = 31.32 \text{ m/s}

Explanation:

This follows from v² = u² + 2as with a = g and s = h. It is equivalent to conservation of mechanical energy when only gravity does work.

3

Calculate Time of Fall

Solve the displacement equation for time (take the positive root):

Equation:

h=v0t+12gt2h = v_0 t + \frac{1}{2}gt^2

Calculation:

12(9.81)t2+0t−50=0\frac{1}{2}(9.81)t^2 + 0t - 50 = 0
t=−0+02+2(9.81)(50)9.81t = \frac{-0 + \sqrt{0^2 + 2(9.81)(50)}}{9.81}
t=3.19 st = 3.19 \text{ s}

Result:

t=3.19 st = 3.19 \text{ s}

Explanation:

The quadratic has two roots; the physically meaningful one is positive and corresponds to the object reaching the ground moving downward.

4

Verify with Average Velocity

Check consistency using average speed for uniformly accelerated motion:

Equation:

vavg=ht=v0+v2v_{avg} = \frac{h}{t} = \frac{v_0 + v}{2}

Calculation:

vavg=503.19=15.66 m/sv_{avg} = \frac{50}{3.19} = 15.66 \text{ m/s}
v0+v2=0+31.322=15.66 m/s\frac{v_0 + v}{2} = \frac{0 + 31.32}{2} = 15.66 \text{ m/s}

Result:

vavg=15.66 m/sv_{avg} = 15.66 \text{ m/s}

Explanation:

For constant acceleration, mean velocity equals the arithmetic average of initial and final speeds.

Frequently Asked Questions (FAQ)

Does mass affect free fall?

In vacuum, all objects fall with the same acceleration regardless of mass (Galileo's principle). With air resistance, lighter objects fall slower in practice.

Why is g ≈ 9.81 m/s²?

It is the average gravitational acceleration at Earth's surface, combining the planet's mass and radius: g = GM/R².

Can initial velocity be upward?

This calculator models downward launch (v₀ ≥ 0 downward). Upward throws require sign conventions and may return to the release height before falling.

Why take the positive root for time?

The quadratic in t has two roots; the positive one corresponds to the object reaching the ground moving downward after a positive elapsed time.

Practice MCQs

  1. Doubling the drop height (from rest) multiplies impact speed by:
  2. In free fall (no drag), acceleration is:
  3. From rest, time to fall is proportional to:

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