Projectile Motion Examples in Physics

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

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

Concept Recap

Two-dimensional motion under gravity alone, where horizontal velocity is constant and vertical motion is uniformly accelerated — producing a parabolic path.

A thrown ball follows a curved path—horizontal motion is steady, vertical is accelerated.

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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: Projectile Motion starts by naming what changes, over what time interval, and whether direction matters.

Common stuck point: Students often know a formula related to projectile motion 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

medium

A ball is launched horizontally at

15 \text{ m/s}

from a cliff

45 \text{ m}

high. How far from the base of the cliff does it land? Use

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

How far from the base of the cliff does it land?

Answer

x = 45 \text{ m}

First step

Use vertical motion to find the time to fall:

t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 45}{10}} = \sqrt{9} = 3 \text{ s}

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Example 2

hard

A projectile is launched at

40 \text{ m/s}

30°

above the horizontal. What is the maximum height and horizontal range? Use

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

Find maximum height and horizontal range.

Example 3

medium

A projectile is launched at

30 \text{ m/s}

30°

above the horizontal (

g = 10

\sin 30° = 0.5

). Find the maximum height above launch.

Find the maximum height above launch.

Example 4

medium

A ball is thrown horizontally at

15 \text{ m/s}

from a

25 \text{ m}

cliff (

g = 10

). Find the landing time and horizontal distance.

Find the landing time and horizontal distance.

Example 5

medium

A ball thrown horizontally at

20 \text{ m/s}

from a

20 \text{ m}

cliff (

g = 10

). Find its speed just before landing.

Example 6

hard

A soccer ball is kicked at

25 \text{ m/s}

with

\sin\theta = 0.6

\cos\theta = 0.8

(

g = 10

). Find the range on level ground and the time of flight.

Find the total flight time and horizontal range.

Example 7

hard

A stunt rider launches off a horizontal ramp at

20 \text{ m/s}

horizontally. The landing ramp is

5 \text{ m}

lower. Using

g = 10

, find the horizontal distance until landing.

Find the horizontal distance to the landing point.

Example 8

challenge

A ball is kicked off a

20 \text{ m}

cliff at

20 \text{ m/s}

30°

above horizontal (

g = 10

\sin 30° = 0.5

\cos 30° \approx 0.866

). Find the time to hit the ground below.

Practice Problems

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

Example 1

medium

A ball is kicked at

20 \text{ m/s}

45°

. What is the range? Use

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

Find the range on level ground.

Example 2

hard

A ball is kicked horizontally off a

45 \text{ m}

high cliff at

20 \text{ m/s}

. Using

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

: (a) How long until it hits the ground? (b) How far from the base of the cliff does it land?

Find (a) time to hit the ground and (b) horizontal distance from base.

Example 3

easy

A ball is launched horizontally at

10

m/s. What is its horizontal velocity after

3

s (no air resistance)?

Example 4

easy

A projectile is launched horizontally from a cliff. What is its initial vertical velocity?

Example 5

easy

A ball rolls off a table and falls for

1

s (

g=10

). How far does it drop vertically?

Example 6

easy

A projectile launched at speed

v_0

at angle

\theta

. Write its initial horizontal velocity.

The horizontal component of launch velocity is v₀cosθ.

Example 7

easy

A ball is thrown horizontally at

8

m/s and is in the air

2

s. Horizontal distance?

Example 8

easy

At the highest point of a projectile's arc, what is its vertical velocity?

Example 9

easy

A projectile's launch speed is

20

m/s at

30°

. Find

v_{0y}

(

\sin30°=0.5

Find v₀y = v₀ sin 30°.

Example 10

easy

Why does a horizontally-thrown ball and a dropped ball hit the ground at the same time (same height)?

Example 11

medium

A ball thrown horizontally at

15

m/s from a

20

m cliff (

g=10

). Find the time to land.

How long does the ball take to reach the ground?

Example 12

medium

Continuing: that

15

m/s ball from a

20

m cliff with

t=2

s. Find the horizontal range.

Find the horizontal distance from the base (t = 2 s).

Example 13

medium

A projectile launched at

20

m/s,

30°

(

g=10

\sin30°=0.5

). Find the time to reach maximum height.

How long does the projectile take to reach maximum height?

Example 14

medium

For the

20

m/s,

30°

projectile (

g=10

), find the maximum height above launch.

Find the maximum height above launch.

Example 15

medium

A ball is kicked at

25

m/s at angle with

\cos\theta=0.8

\sin\theta=0.6

. Find

v_{0x}

and

v_{0y}

Find v₀x and v₀y for the 25 m/s launch.

Example 16

medium

For the full flight (lands at launch height) of the

20

m/s,

30°

projectile (

g=10

), find the total flight time.

Find the total flight time for the full arc on level ground.

Example 17

challenge

A projectile launched at

20

m/s,

30°

over level ground (

g=10

). Find the horizontal range.

Find the horizontal range on level ground.

Example 18

challenge

A ball thrown horizontally at

20

m/s from a

45

m cliff (

g=10

). Find its speed just before landing.

Example 19

challenge

Two balls leave a table edge horizontally, one at

4

m/s and one at

8

m/s. Compare their fall times and landing distances (table height fixed).

Example 20

medium

A ball rolls off a

5

m high table at

6

m/s horizontally (

g=10

). Find the time to land.

How long does the ball take to hit the floor?

Example 21

medium

The same

6

m/s ball (

t=1

s) — find its horizontal distance from the table base.

Find the horizontal distance from the table base (t = 1 s).

Example 22

medium

A projectile is launched at

50

m/s with

\sin\theta=0.6

\cos\theta=0.8

. Find

v_{0x}

and

v_{0y}

Find v₀x and v₀y for the 50 m/s launch.

Example 23

easy

A stone is dropped (no horizontal kick) from

20 \text{ m}

. Using

g = 10

, find the time to land.

Example 24

easy

A ball rolls off a table at

5 \text{ m/s}

. After

0.4 \text{ s}

, what is its horizontal velocity (ignore air drag)?

Example 25

easy

A ball thrown horizontally at

12 \text{ m/s}

is in the air for

1.5 \text{ s}

. Find the horizontal distance.

Find the horizontal distance (t = 1.5 s).

Example 26

easy

Two balls leave the same table at the same instant. Ball A is dropped, ball B is thrown horizontally at

4 \text{ m/s}

. Which lands first?

Example 27

medium

A ball is launched at

30 \text{ m/s}

30°

(

g = 10

). Find the total flight time on level ground.

Find the total flight time on level ground.

Example 28

medium

For the same

30 \text{ m/s}

30°

launch (

g = 10

\cos 30° \approx 0.866

), find the horizontal range on level ground.

Find the horizontal range on level ground.

Example 29

medium

Find

v_{0x}

and

v_{0y}

for a launch at

50 \text{ m/s}

with

\cos\theta = 0.8

\sin\theta = 0.6

Find v₀x and v₀y.

Example 30

medium

Using the launch from X13 (

50 \text{ m/s}

\cos\theta=0.8

\sin\theta=0.6

g = 10

), find the time to peak height.

Find the time to reach maximum height.

Example 31

medium

Continuing X13–X14: find the maximum height above launch.

Find the maximum height above launch.

Example 32

medium

A projectile is launched at

20 \text{ m/s}

60°

(

g = 10

\sin 60° \approx 0.866

\cos 60° = 0.5

). Find the maximum height.

Find the maximum height above launch.

Example 33

medium

Compare ranges for projectiles launched on level ground at the same

v_0

30°

60°

. Which is greater?

Example 34

medium

A ball rolls off a

1.25 \text{ m}

high table at

3 \text{ m/s}

horizontally (

g = 10

). How far from the table base does it land?

How far from the table base does the ball land?

Example 35

hard

A projectile launched at

40 \text{ m/s}

45°

from level ground (

g = 10

\sin 45° = \cos 45° \approx 0.707

). Find the peak height.

Find the maximum height above launch.

Example 36

hard

Continuing X22: find the range on level ground.

Find the horizontal range on level ground.

Example 37

challenge

A projectile is fired from ground level at

50 \text{ m/s}

with

\sin\theta = 0.6

\cos\theta = 0.8

(

g = 10

). At what TWO times is the projectile at height

30 \text{ m}

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Related Concepts

Free Fall Velocity Vectors Circular Motion

Background Knowledge

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

free fallvelocityvectors