Physics

1.19 - Projectile Motion

5 min

note 1 of 5

What a projectile is and why its path curves

A projectile is an object that's only acted on by gravity once it's moving (air resistance is assumed to be negligible).
An object dropped from rest is a projectile, and so is an object launched horizontally.

Why a horizontally launched projectile curves

Its horizontal velocity stays constant because no horizontal force acts on it.
It has a constant vertical acceleration downwards, due to gravity, so its vertical velocity increases as it falls.

A stick figure on a tall building, with a ball at three points on a dashed curved path, equal horizontal arrows and lengthening downward arrows labelled constant horizontal velocity and increasing vertical velocity.

note 2 of 5

Treating horizontal and vertical motion separately

The horizontal and vertical motions of a projectile are independent, so they're calculated separately.

Horizontal motion - Constant velocity

$v_{h} = \frac{s}{t}$

Where:

$v_{h}$ = Horizontal velocity, in metres per second (m/s)
$s$ = Horizontal displacement, in metres (m)
$t$ = Time, in seconds (s)

Vertical motion - Constant acceleration

$v_{v} = u_{v} + a t$

Where:

$v_{v}$ = Final vertical velocity, in metres per second (m/s)
$u_{v}$ = Initial vertical velocity, in metres per second (m/s); for a projectile launched horizontally, $u_{v} = 0$
$a$ = Vertical acceleration, in metres per second squared (m/s²), equal to $g$
$t$ = Time, in seconds (s)

note 3 of 5

Worked example - Horizontally launched projectile

A stone is thrown horizontally from the top of a cliff at 15 m/s. Its vertical velocity just as it hits the ground below is 24.5 m/s. Take $g$ = 9.8 m/s² and assume no air resistance. Find the time to reach the ground, then the horizontal distance travelled.

A ball with a downward arrow labelled vertical velocity = 24.5 m/s, a right-pointing arrow labelled horizontal velocity = 15 m/s, and a second downward arrow below labelled g = 9.8 m/s².

Step 1 - Identify the values

Horizontal velocity, $v_{h} = 15$ m/s
Final vertical velocity, $v_{v} = 24.5$ m/s
Initial vertical velocity, $u_{v} = 0$ m/s (launched horizontally)
Vertical acceleration, $a = g = 9.8$ m/s²

Step 2 - Find the time using the vertical motion

$v_{v} = u_{v} + a t$

$24.5 = 0 + (9.8 \times t)$

$t = \frac{24.5}{9.8} = 2.5 s$

Step 3 - Find the horizontal distance

The horizontal velocity is constant, so use $v_{h} = \frac{s}{t}$ :

$s = v_{h} \times t = 15 \times 2.5 = 37.5 m$

note 4 of 5

Velocity-time graphs for a projectile

A projectile launched horizontally is represented by two separate velocity-time graphs:

The horizontal graph is a flat horizontal line, showing constant horizontal velocity.
The vertical graph is a straight line sloping upwards, showing constant vertical acceleration of $g$ .

Area under each graph

Area under the horizontal graph = range (horizontal distance travelled).
Area under the vertical graph = height (vertical distance travelled).

Two velocity against time graphs side by side, separated by a dashed line: the one labelled horizontal is a flat line, and the one labelled vertical is a straight line rising from the origin.

note 5 of 5

Satellites as projectiles

A satellite is a projectile in free-fall around Earth: the only force acting on it is its weight due to gravity.
Because space is a vacuum, there's no air resistance and its horizontal velocity stays constant.

Why a satellite orbits

The Earth's surface is curved.
A satellite launched fast enough follows a curved path that matches the curvature of the Earth.
It falls towards Earth without ever getting closer to the surface, keeping it in orbit.

Orbital speed

Too slow - The satellite falls back to Earth.
Too fast - The path doesn't curve enough and the satellite escapes into space.
Correct speed - The satellite stays in a stable orbit.

Earth at the centre with three satellites on dashed paths, labelled correct horizontal velocity, too slow (falls to ground), and too fast (flies off), with pink arrows pointing at Earth, one labelled gravity.

key terms

TermDefinition

ProjectileAn object that is only acted on by gravity once it is moving.

RangeThe horizontal distance travelled by a projectile.

end of notes

Key points to remember

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2.1 - The Solar System & the UniverseNext up

Physics

1.19 - Projectile Motion

5 min

note 1 of 5

What a projectile is and why its path curves

A projectile is an object that's only acted on by gravity once it's moving (air resistance is assumed to be negligible).
An object dropped from rest is a projectile, and so is an object launched horizontally.

Why a horizontally launched projectile curves

Its horizontal velocity stays constant because no horizontal force acts on it.
It has a constant vertical acceleration downwards, due to gravity, so its vertical velocity increases as it falls.

note 2 of 5

Treating horizontal and vertical motion separately

The horizontal and vertical motions of a projectile are independent, so they're calculated separately.

Horizontal motion - Constant velocity

$v_{h} = \frac{s}{t}$

Where:

$v_{h}$ = Horizontal velocity, in metres per second (m/s)
$s$ = Horizontal displacement, in metres (m)
$t$ = Time, in seconds (s)

Vertical motion - Constant acceleration

$v_{v} = u_{v} + a t$

Where:

$v_{v}$ = Final vertical velocity, in metres per second (m/s)
$u_{v}$ = Initial vertical velocity, in metres per second (m/s); for a projectile launched horizontally, $u_{v} = 0$
$a$ = Vertical acceleration, in metres per second squared (m/s²), equal to $g$
$t$ = Time, in seconds (s)

note 3 of 5

Worked example - Horizontally launched projectile

Step 1 - Identify the values

Horizontal velocity, $v_{h} = 15$ m/s
Final vertical velocity, $v_{v} = 24.5$ m/s
Initial vertical velocity, $u_{v} = 0$ m/s (launched horizontally)
Vertical acceleration, $a = g = 9.8$ m/s²

Step 2 - Find the time using the vertical motion

$v_{v} = u_{v} + a t$

$24.5 = 0 + (9.8 \times t)$

$t = \frac{24.5}{9.8} = 2.5 s$

Step 3 - Find the horizontal distance

The horizontal velocity is constant, so use $v_{h} = \frac{s}{t}$ :

$s = v_{h} \times t = 15 \times 2.5 = 37.5 m$

note 4 of 5

Velocity-time graphs for a projectile

A projectile launched horizontally is represented by two separate velocity-time graphs:

The horizontal graph is a flat horizontal line, showing constant horizontal velocity.
The vertical graph is a straight line sloping upwards, showing constant vertical acceleration of $g$ .

Area under each graph

Area under the horizontal graph = range (horizontal distance travelled).
Area under the vertical graph = height (vertical distance travelled).

note 5 of 5

Satellites as projectiles

A satellite is a projectile in free-fall around Earth: the only force acting on it is its weight due to gravity.
Because space is a vacuum, there's no air resistance and its horizontal velocity stays constant.

Why a satellite orbits

The Earth's surface is curved.
A satellite launched fast enough follows a curved path that matches the curvature of the Earth.
It falls towards Earth without ever getting closer to the surface, keeping it in orbit.

Orbital speed

Too slow - The satellite falls back to Earth.
Too fast - The path doesn't curve enough and the satellite escapes into space.
Correct speed - The satellite stays in a stable orbit.

key terms

TermDefinition

ProjectileAn object that is only acted on by gravity once it is moving.

RangeThe horizontal distance travelled by a projectile.

end of notes

Key points to remember

Take a quiz View flashcards

2.1 - The Solar System & the UniverseNext up