Physics 9702 · Paper 1

Projectiles: Two Independent Motions

A is an object thrown or launched and then left to gravity alone.
Its motion splits into two separate problems: constant velocity across, constant acceleration down. The only quantity the two share is the time.

Why the two directions are separate

Gravity pulls straight down. There is no horizontal force (air resistance is ignored), so the horizontal velocity never changes.
The vertical motion is ordinary free fall: acceleration $g$ downward, whatever the horizontal motion is doing.

Horizontal velocity stays the same for the whole flight (gold). Vertical velocity shrinks to zero at the top, then grows downward (blue up, red down). Gravity points straight down the whole time.

The test of this idea: drop one ball and throw another sideways from the same height at the same instant. They land together. The sideways throw does not change the fall.

The sideways throw does not change the fall. At every instant both balls are at the same height (dashed links), so they hit the floor at the same time.

Where the independence comes from

Newton's second law works direction by direction. The only force is gravity, which acts straight down, so only the vertical velocity changes. The horizontal direction has no force, so no acceleration, so constant velocity for the whole flight.

Splitting the launch velocity

A launch at angle $\theta$ is resolved once, at the start, using the components from lesson 1.8:

u_H = v\cos\theta \qquad u_V = v\sin\theta

Symbols

$v$ = launch speed (m s⁻¹)
$\theta$ = launch angle above the horizontal (degrees)
$u_H$ = horizontal component (stays constant) (m s⁻¹)
$u_V$ = initial vertical component (changes under g) (m s⁻¹)

Split the launch velocity once, at the start: v cos θ across (this never changes) and v sin θ up (gravity changes this). Drawn to scale at θ = 35°.

Drag the launch speed and angle below to see the two motions run at the same time:

Projectile Explorer

Drag the sliders. Notice the horizontal component (green) only changes with the angle, never during the flight — gravity acts on the vertical (red) alone.

Launch speed v20 m s⁻¹

Launch angle θ45°

uₕ = v cos θ

14.1 m s⁻¹

uᵥ = v sin θ

14.1 m s⁻¹

time of flight

2.88 s

range R

40.8 m

Your turn— tap to reveal the worked answer (9702/11/M/J/24 Q7)

A golf ball flies through the air; air resistance is ignored. Describe what happens to the horizontal and the vertical components of its velocity. (9702/11/M/J/24 Q7)

Answer: the horizontal component does not change (no horizontal force). The vertical component changes the whole time: it decreases on the way up, is zero at the top, then increases downward.

Solve every projectile as two separate motions joined by one shared time: constant velocity across, free fall down.

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Projectiles: Two Independent Motions

A is an object thrown or launched and then left to gravity alone.
Its motion splits into two separate problems: constant velocity across, constant acceleration down. The only quantity the two share is the time.

Why the two directions are separate

Gravity pulls straight down. There is no horizontal force (air resistance is ignored), so the horizontal velocity never changes.
The vertical motion is ordinary free fall: acceleration $g$ downward, whatever the horizontal motion is doing.

Horizontal velocity stays the same for the whole flight (gold). Vertical velocity shrinks to zero at the top, then grows downward (blue up, red down). Gravity points straight down the whole time.

The test of this idea: drop one ball and throw another sideways from the same height at the same instant. They land together. The sideways throw does not change the fall.

The sideways throw does not change the fall. At every instant both balls are at the same height (dashed links), so they hit the floor at the same time.

Where the independence comes from

Splitting the launch velocity

A launch at angle $\theta$ is resolved once, at the start, using the components from lesson 1.8:

u_H = v\cos\theta \qquad u_V = v\sin\theta

Symbols

$v$ = launch speed (m s⁻¹)
$\theta$ = launch angle above the horizontal (degrees)
$u_H$ = horizontal component (stays constant) (m s⁻¹)
$u_V$ = initial vertical component (changes under g) (m s⁻¹)

Split the launch velocity once, at the start: v cos θ across (this never changes) and v sin θ up (gravity changes this). Drawn to scale at θ = 35°.

Drag the launch speed and angle below to see the two motions run at the same time:

Projectile Explorer

Drag the sliders. Notice the horizontal component (green) only changes with the angle, never during the flight — gravity acts on the vertical (red) alone.

Launch speed v20 m s⁻¹

Launch angle θ45°

uₕ = v cos θ

14.1 m s⁻¹

uᵥ = v sin θ

14.1 m s⁻¹

time of flight

2.88 s

range R

40.8 m

Your turn— tap to reveal the worked answer (9702/11/M/J/24 Q7)

A golf ball flies through the air; air resistance is ignored. Describe what happens to the horizontal and the vertical components of its velocity. (9702/11/M/J/24 Q7)

Answer: the horizontal component does not change (no horizontal force). The vertical component changes the whole time: it decreases on the way up, is zero at the top, then increases downward.

Solve every projectile as two separate motions joined by one shared time: constant velocity across, free fall down.