--- title: "Projectile Motion" description: "Split the launch velocity into horizontal and vertical parts, then run constant velocity across and constant acceleration downwards, with time as the only quantity the two share. Range, greatest heigh" canonical: https://lightmysky.com/learn/mathematics/projectile-motion-mt_O1C-QxCSJN source: https://lightmysky.com/learn/mathematics/projectile-motion-mt_O1C-QxCSJN.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Projectile Motion Split the launch velocity into horizontal and vertical parts, then run constant velocity across and constant acceleration downwards, with time as the only quantity the two share. Range, greatest height and flight time follow. Subject: Mathematics · Area: Mechanics · Ages 17 to 18 Page: https://lightmysky.com/learn/mathematics/projectile-motion-mt_O1C-QxCSJN ## Ready when they can - Split a launch speed and angle into horizontal and vertical components - Find the time of flight from the vertical motion, then the range from the horizontal - Say what the model assumes by leaving air resistance out ## Lesson: Two lives of a flying ball Kick a ball into the air and split its flight in two: sideways and up-and-down. Split the launch into v cos(theta) across and v sin(theta) up: 25 m/s with cos 0.8 and sin 0.6 gives 20 across and 15 up. Then run two independent lives: constant velocity across, constant acceleration down, with time the only quantity both share. **Example.** With vertical speed 15 m/s and g = 10, rising takes 15/10 = 1.5 s and symmetric flight doubles it to 3 s. Range is horizontal speed times time: 20 times 3 = 60 m. Greatest height uses v squared = u squared + 2as with v = 0: 225/20 = 11.25 m. At the very top the vertical velocity is zero, the instant rising turns to falling. With no air resistance nothing pushes across, so horizontal velocity stays constant all flight. The model assumes gravity alone: no drag, constant g, flat ground. Because real drag slows the ball, leaving it out makes the predicted range too long. **Tip.** Real drag bites hardest at speed and steals range, so ignoring it overestimates how far the ball lands. The same steps handle 20 m/s at 30 degrees: vertical 10 m/s gives 2 s of flight, and 17.32 m/s across gives about 34.6 m. State the assumptions to show where the maths ends and the world begins. **Recap.** Split the launch into across and up, time the vertical life, then spend that time crossing. ## Practice 18 questions on this page, each with its working shown. ## Needs first - [Vertical Motion Under Gravity](https://lightmysky.com/learn/mathematics/vertical-motion-under-gravity-mt_IgNj9bn14O) - [Trigonometry basics](https://lightmysky.com/learn/mathematics/trigonometry-basics-mt_KB_Czd7RQH) - [Sketching Quadratic Graphs from Roots and the Turning Point](https://lightmysky.com/learn/mathematics/sketching-quadratic-graphs-from-roots-and-the-turning-point-mt_RcrJIbbN2x) ## Opens up - [Vector-Valued Functions and Motion Along a Curve](https://lightmysky.com/learn/mathematics/vector-valued-functions-and-motion-along-a-curve-mt_Xcjt6exMy3)