Free Fall Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Free Fall.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Motion under gravity alone, with no air resistance — all objects in free fall accelerate at $g \approx 9.81$ m/s² regardless of mass.

A dropped ball accelerates at the same rate regardless of its mass.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Free Fall starts by naming what changes, over what time interval, and whether direction matters.

Common stuck point: Students often know a formula related to free fall but skip the recognition step: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated?

Worked Examples

Example 1

easy

A stone is dropped from a cliff. How far does it fall in

3 \text{ s}

? Use

g = 9.8 \text{ m/s}^2

Answer

d = 44.1 \text{ m}

First step

Initial velocity:

v_0 = 0

(dropped from rest).

Full solution

2
Use the free-fall displacement equation: $d = v_0 t + \frac{1}{2}gt^2$ .
3
$d = 0 + \frac{1}{2}(9.8)(9) = 44.1 \text{ m}$

In free fall, the only force acting is gravity. All objects fall at the same rate regardless of mass (ignoring air resistance), accelerating at

g = 9.8 \text{ m/s}^2

Example 2

medium

A ball is thrown upward with an initial velocity of

20 \text{ m/s}

. How high does it go, and how long until it returns? Use

g = 9.8 \text{ m/s}^2

Example 3

medium

A stone is dropped from a

125 \text{ m}

tall cliff. Find its impact speed. Use

g = 10 \text{ m/s}^2

Example 4

hard

A pebble dropped from rest falls a distance of

\tfrac{3}{4}

of the total height in the LAST second of its fall. Find the total time and height. Use

g = 10 \text{ m/s}^2

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

An object is dropped from a height of

80 \text{ m}

. How long does it take to hit the ground? Use

g = 10 \text{ m/s}^2

Example 2

medium

A ball is thrown straight up with an initial velocity of

20 \text{ m/s}

. Using

g = 10 \text{ m/s}^2

: (a) How long until it reaches its highest point? (b) What maximum height does it reach? (c) What is its velocity when it returns to the starting height?

Example 3

easy

A ball is dropped from rest. Find its speed after

2

s (

g=9.8

m/s

^2

Example 4

easy

How far does a dropped object fall in

3

s (

g=9.8

m/s

^2

Example 5

easy

On the Moon a feather and a hammer are dropped together. Which lands first?

Example 6

easy

Use

g=10

m/s

^2

. A stone dropped from rest reaches what speed after

4

Example 7

easy

A ball thrown straight up momentarily stops at the top. What is its acceleration there (

g=9.8

Example 8

easy

A rock falls from rest for

1

s (

g=9.8

). How far does it fall?

Example 9

easy

Define free fall in one phrase.

Example 10

easy

A ball is thrown down at

5

m/s (

g=9.8

). Its speed after

2

Example 11

medium

A ball is dropped from

20

m (

g=10

). How long to hit the ground?

Example 12

medium

A stone is thrown up at

19.6

m/s (

g=9.8

). What maximum height does it reach?

Example 13

medium

A ball thrown up at

19.6

m/s returns to launch height. Total flight time (

g=9.8

Example 14

medium

A ball dropped from a cliff hits the ground at

30

m/s (

g=10

). How tall is the cliff?

Example 15

medium

With

g=9.8

, how much does the speed of a dropped object increase each second?

Example 16

medium

A ball is dropped from rest. How far does it fall during the THIRD second (

g=10

Example 17

challenge

A ball is thrown up from the ground at

30

m/s (

g=10

). At what times is it at height

40

Example 18

challenge

Two balls are released from the same point at height

80

m. The first is dropped from rest;

1

second later, the second is thrown straight down at

20

m/s. Using

g = 10

m/s², does the second ball catch the first before either lands?

Example 19

challenge

A ball dropped from height

H

falls the last

25\%

H

in the final second of a

4

s fall (

g=10

). Verify with

H

Example 20

medium

A ball is dropped from rest and reaches

24.5

m/s (

g=9.8

). How long did it fall?

Example 21

medium

A stone thrown down at

4

m/s (

g=10

) falls

48

m. Find its landing speed.

Example 22

medium

A ball thrown up at

14

m/s (

g=9.8

). Find its speed after

1

Example 23

easy

A ball is dropped from rest. What is its velocity after

5 \text{ s}

? Use

g = 10 \text{ m/s}^2

Example 24

easy

An object falls from rest for

0.5 \text{ s}

. How far has it fallen? Use

g = 10 \text{ m/s}^2

Example 25

easy

How long does an object dropped from rest take to reach

30 \text{ m/s}

? Use

g = 10 \text{ m/s}^2

Example 26

easy

A rock thrown straight up at

25 \text{ m/s}

reaches maximum height. What is its velocity at that instant? Use

g = 9.8 \text{ m/s}^2

Example 27

medium

A ball is thrown straight up at

15 \text{ m/s}

. How long until it returns to the launch height? Use

g = 10 \text{ m/s}^2

Example 28

medium

A ball thrown up at

20 \text{ m/s}

from the ground returns. What is its speed just before landing? Use

g = 10 \text{ m/s}^2

Example 29

medium

A ball is dropped from rest. How far does it fall during the FIRST second? Use

g = 9.8 \text{ m/s}^2

Example 30

medium

A ball is dropped from a

20 \text{ m}

height. How fast is it moving halfway down? Use

g = 10 \text{ m/s}^2

Example 31

medium

An object is thrown straight up at

40 \text{ m/s}

. At what time(s) is it

60 \text{ m}

above the ground? Use

g = 10 \text{ m/s}^2

Example 32

medium

A ball is dropped from rest. What is the ratio of distances fallen in the 1st, 2nd, and 3rd seconds?

Example 33

medium

A ball is thrown up at

9.8 \text{ m/s}

. How high above launch does it rise? Use

g = 9.8 \text{ m/s}^2

Example 34

hard

A coin is dropped down a well and the splash is heard

3 \text{ s}

later. Ignoring sound travel time, how deep is the well? Use

g = 10 \text{ m/s}^2

Example 35

hard

A ball is thrown up from a

25 \text{ m}

rooftop at

20 \text{ m/s}

. Find its speed just before hitting the ground. Use

g = 10 \text{ m/s}^2

Example 36

hard

A ball is thrown up from the ground at

30 \text{ m/s}

. How long does it spend above

25 \text{ m}

? Use

g = 10 \text{ m/s}^2

Example 37

hard

A ball is thrown straight up. It takes

3 \text{ s}

to come back down to the launch point. With what speed was it thrown? Use

g = 10 \text{ m/s}^2

Example 38

hard

A stone dropped from rest passes a

10 \text{ m}

tall window in

0.5 \text{ s}

. From what height above the top of the window was it released? Use

g = 10 \text{ m/s}^2

Example 39

hard

Ball A is dropped from a height

h

. At the same instant Ball B is thrown up from the ground directly below at

v_0

. They collide at half height. Find

v_0

in terms of

h

and

g

Example 40

hard

A rocket accelerates upward at

20 \text{ m/s}^2

for

4 \text{ s}

, then engines cut off. How high does it rise in total above launch? Use

g = 10 \text{ m/s}^2

thereafter.

Example 41

hard

A ball is dropped from a

45 \text{ m}

height. What fraction of the total fall distance does it cover in the LAST second? Use

g = 10 \text{ m/s}^2

Example 42

challenge

A ball is thrown up from the ground at

v_0

and another is dropped from height

h

at the same instant. They collide exactly at the moment the upward ball reaches its peak. Find

h

in terms of

v_0

and

g

Example 43

challenge

A ball is dropped from height

H

onto a hard floor and rebounds to height

H/4

(no air resistance). What fraction of its kinetic energy is lost in the bounce?

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Related Concepts

Acceleration Projectile Motion Gravity

Background Knowledge

These ideas may be useful before you work through the harder examples.

acceleration