Independent horizontal & vertical motion
Use one clock to combine independent horizontal and vertical models.
Drop one ball and launch another sideways.
Need an earlier step? Start with free fall & vertical launches →
Release two balls from a 5 m shelf at the same time. One has no horizontal velocity; the other starts at 3 m/s horizontally. Both start with zero vertical velocity. Neglect air resistance and use g = 10 m/s².
Words and symbols you will use
- Horizontal x / vertical y
- Perpendicular directions that describe the same object’s motion.
- Independent components
- Horizontal velocity does not enter the vertical-motion equation in this model.
- Shared time t
- Both component descriptions use the same elapsed time.
Read the picture, one step at a time.
- At 0.5 s, both balls have fallen 1.25 m. The sideways ball has also moved 1.5 m horizontally.
- At 1 s, both have fallen 5 m and reach the ground together.
- Horizontal motion changes the landing location, not the flight time when the vertical starting conditions match.
| Compare | What it means | What follows |
|---|---|---|
| Horizontal | aₓ = 0 | vₓ stays constant; Δx = vₓt. |
| Vertical | aᵧ = −g | vᵧ changes; Δy = vᵧ₀t − ½gt². |
The idea to keep: Equal landing times require the same initial height, vertical velocity, landing level and gravity. A ball launched upward is a different vertical starting condition.
Why does horizontal motion not change the time to fall?
In the ideal projectile model, vertical motion is set by initial height, initial vertical velocity and gravity. Horizontal velocity does not appear in the vertical equation.
Track the horizontal and vertical coordinates using the same clock. With no air resistance, horizontal acceleration is zero while vertical acceleration is −g. The two components can be analyzed separately and combined to locate the projectile at a given time.
Independence is conditional on the model. Wind, drag, lift or contact forces can change the motion. Also, increasing launch speed at a fixed nonzero angle changes the vertical component, so it can change flight time. “Horizontal motion does not matter” is not a license to ignore the launch geometry.
A reliable approach
- Split the initial velocity into horizontal and vertical components.
- Write one equation for each coordinate, with a shared time variable.
- Find flight time from the vertical condition, then use it horizontally.
Work through one example.
Two balls start 20 m above level ground with zero vertical velocity. One is dropped; the other moves horizontally at 6 m/s. With g = 10 m/s², compare landing times and positions.
Follow the worked solution
- Both obey 0 = 20 − 5t², so both land at t = 2 s.
- Dropped ball has no horizontal displacement.
- Launched ball travels 6(2) = 12 m horizontally.
Equal landing times require matching initial vertical conditions and matching landing height, with the same gravitational acceleration and negligible air resistance.
Explain it without notes: Explain why changing speed at a fixed upward angle can change flight time.
Try explaining it now.
Two balls have identical vertical launch conditions but different horizontal speeds. Which lands first on level ground?
Compare with an explanation
They land together in the ideal model. Their vertical equations match. Their horizontal ranges can be different.
Another explanation, if you need oneOptional external lesson · Flipping Physics
Two-dimensional and projectile motion
This lesson is complete without a video. For another teacher’s explanation, open the original resource below. Pause after a diagram and explain the idea in your own words.
Suggested section 16:57–20:13. Video by Flipping Physics / Jonathan Thomas-Palmer. Refresh Kid is not affiliated with or endorsed by Flipping Physics. These links open another website. Some videos use g = 9.81 m/s²; our examples state g = 10 m/s². Follow the value given in each problem.
After watching: Explain why changing speed at a fixed upward angle can change flight time.
Make a prediction. Test it.
Keep vertical speed and launch height fixed; change horizontal speed. Watch the vertical shadow and landing time stay unchanged while the range changes.
Motion graphs · same clock, different quantities
Try two questions.
Two original Refresh Kid questions. Choose an answer, explain it to yourself, then check the reasoning. These are not released AP exam questions.
Show your reasoning.
Original mini-FRQ · 4 points · Self-checkBalls A and B are launched horizontally from height H with horizontal speeds u and 2u.
- Derive fall time.
- Compare ranges.
- Compare their vertical velocities just before impact.
- Explain the physical reason for the time comparison.
Your response stays on this page and is not submitted or automatically graded. Copy it before leaving.
Compare with the worked solution & scoring guide
- 1 point: t = √(2H/g).
- 1 point: R_A = u√(2H/g); R_B = 2R_A.
- 1 point: Both have v_y = −√(2gH).
- 1 point: Matching vertical initial conditions and acceleration give identical vertical motion.
Accept an equivalent correct method. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What is horizontal acceleration in the ideal model?
Zero.
RECALL 2What is vertical acceleration at the apex?
−g when up is positive.
RECALL 3When do two projectiles have equal flight times?
When their initial vertical conditions and landing height match under the same ideal model.
Come back tomorrow: answer these with the cards closed. Try again a week later, especially the ones you missed.
Keep the key ideas handy.
Independent horizontal & vertical motion
Core idea: In the ideal projectile model, vertical motion is set by initial height, initial vertical velocity and gravity. Horizontal velocity does not appear in the vertical equation.
- x = x₀ + v_x0t when a_x = 0.
- y = y₀ + v_y0t − ½gt²
- One shared time connects both components.
Avoid this: Equal landing times require matching initial vertical conditions and matching landing height, with the same gravitational acceleration and negligible air resistance.
Remember why: Equal landing times require the same initial height, vertical velocity, landing level and gravity. A ball launched upward is a different vertical starting condition.
Match initial height, vertical velocity, gravity and landing height before comparing times.
Explain, don’t just substituteExplain why changing speed at a fixed upward angle can change flight time.
Refresh Kid · AP Physics 1 · Unit 1 · 1.5.B · Check units, direction and model assumptions.
Connect to released AP practice.
2026 · Question 1 · Version J
Use Part A(i) for component velocity graphs and Part A(ii) for a kinematics derivation. The remaining parts use fluid concepts from Unit 8; they are not Unit 1-only practice.
This selection directly connects to this lesson. Historical papers may use different timing or course coverage. Official questions remain on College Board’s site; our questions below are original practice.
Browse released years and scoring information ↗Framework alignment: College Board CED, Topic 1.5. Current exam corrections. Checked September 16, 2026. These explanations and practice items are independently authored by Refresh Kid. The simulation is a mathematical model, not experimental data.
About the videos and learning approach
Optional videos are linked to the publisher’s website and YouTube channel with credit. No external video player is loaded on this lesson page. The written lessons, simulations and practice here are independently authored by Refresh Kid.
We combine worked examples, visual models, explanation and recall practice. See the Institute of Education Sciences study guide ↗ for the underlying learning recommendations.
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