Horizontal Projectile Motion – Complete Notes, Revision, Important Questions & Downloads
Horizontal projectile motion is the special case where a body is projected with a purely horizontal initial velocity u from a height H above the ground (θ = 0°). Three subtopics are covered: Trajectory of Horizontal Projectile (y = gx²/2u²), Time of Flight in Horizontal Projection (T = √(2H/g)), and Horizontal Range in Horizontal Projection (R = u√(2H/g)). NEET tests this by asking how far from the cliff base a horizontally launched body lands, the speed of impact, or the angle of velocity at impact. A classic multi-body scenario ('three particles from same height — same or different time?') also appears directly in NEET.
NEET Weightage — Horizontal Projectile Motion
Motion In Two Dimension (Chapter 3)| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2024 | 0 | 0 | |
| 2023 | 1 | 4 | |
| 2022 | 1 | 4 | |
| 2021 | 0 | 0 | |
| 2020 | 1 | 4 | |
| 2019 | 0 | 0 | |
| 6-Year Total (2019–2024) | 2–4 | 8–16 |
Velocity at impact: v_x = u (horizontal, unchanged), v_y = gT = g√(2H/g) = √(2gH). Speed on impact = √(u² + 2gH). This formula connects to energy conservation: (1/2)mv² = (1/2)mu² + mgH.
Angle of velocity at impact: tan(α) = v_y/v_x = √(2gH)/u. NEET may give this angle and ask for u.
How to Prepare Horizontal Projection for NEET
Derive the trajectory equation once to understand the parabola Horizontal: x = ut → t = x/u. Vertical: y = (1/2)gt² = (1/2)g(x/u)² = gx²/(2u²). This is a parabola through the origin with the projectile moving along it from (0,0) downward. NEET may show a curve and ask which axis is x and which is y.
Memorise T = √(2H/g) as the defining formula Time of flight depends only on height H, not on horizontal speed u. This is the key concept: all bodies projected horizontally (at any speed) from the same height land at the same time — only horizontal range differs.
Calculate velocity at impact vectorially v_x = u (horizontal). v_y = gT = g√(2H/g) = √(2gH) (downward). Speed = √(u² + 2gH). Angle with horizontal: tan(α) = v_y/v_x. NEET gives two of these three and asks for the third.
Equal-time conceptual question Three particles A, B, C from same height H: A dropped, B horizontal at 10 m/s, C horizontal at 20 m/s. All reach ground at T = √(2H/g). NEET marks this as assertion: 'They take equal time.' Reason: 'Time depends only on vertical motion.' Both TRUE and reason correctly explains.
Study Materials — Horizontal Projectile Motion
PDF · Cheat Sheet · MCQ Set · PYQSubtopics in Horizontal Projectile Motion
2-Column TableRapid Revision — Horizontal Projectile Motion
Concept → Trap → Example1) Trajectory of Horizontal Projectile
CoreInitial velocity: u (horizontal only, θ = 0°). Horizontal: x = ut. Vertical: y = (1/2)gt². Eliminate t: y = gx²/(2u²). This is a parabola through the origin, opening downward.
- The trajectory y = gx²/(2u²) shows: y ∝ x². On the x-y plane (x = horizontal distance, y = vertical drop), the path curves downward.
- For larger u: same x corresponds to smaller y (the projectile is flatter). The parabola is wider for higher initial speed.
- Important: the vertex of the parabola is at the launch point (0,0). The path never goes above the launch height.
2) Time of Flight in Horizontal Projection
High YieldTime of flight depends only on height H: T = √(2H/g). The horizontal velocity u does not affect T. All bodies projected horizontally from the same height land simultaneously — regardless of their horizontal speed.
- Derivation: vertical motion from height H with u_y = 0 and a = g: H = (1/2)gT² → T = √(2H/g).
- The three-particle result: A (dropped), B (horizontal 10 m/s), C (horizontal 20 m/s) from height H = 20 m all land at T = √(2×20/10) = 2 s simultaneously.
- Trap: 'A ball projected horizontally at higher speed takes longer to fall' — FALSE. T = √(2H/g) is independent of u.
3) Horizontal Range in Horizontal Projection
CoreRange R = u × T = u × √(2H/g) = u√(2H/g). Speed at impact: v = √(u² + v_y²) = √(u² + 2gH). Angle with horizontal: tan(α) = v_y/v_x = √(2gH)/u.
- Range R ∝ u for fixed H: doubling horizontal speed doubles horizontal range.
- Range R ∝ √H for fixed u: to double the range from same u, height must be quadrupled.
- Speed at impact = √(u² + 2gH) — this equals the speed obtained by energy conservation, confirming that mechanical energy is conserved (gravity is conservative).
US Curriculum Gaps — Horizontal Projectile Motion
Topics in this section are tested in NEET but less emphasised in standard US physics courses.Three-Particle Equal-Time Scenario (AP Physics 1 Gap)
AP Physics 1 teaches that time of flight for a horizontal projectile is independent of horizontal speed. However, the explicit three-particle scenario (A dropped, B and C thrown horizontally at different speeds — all from same height) is a direct NEET assertion-reason question format that AP Physics 1 does not drill as a distinct exam type. NEET students must immediately recognise 'same height → same time' as an assertion-reason pair.
- AP Physics 1 covers the concept but does not test it as assertion-reason
- NEET assertion: 'Three particles from same height take same time to land.' Reason: 'Time depends only on vertical free-fall.' Both statements true, reason is correct explanation.
- This appears in NEET about once every 3 years — a reliable 4-mark question for students who drill it.
Trajectory Equation as a Parabola Through Origin (AP Physics C: Mechanics Gap)
AP Physics C covers projectile motion with calculus but does not specifically require memorisation of the trajectory equation y = gx²/(2u²) for horizontal projection or the ability to identify the coefficient of x² to extract initial speed. NEET tests: 'The trajectory of a horizontal projectile is y = 3x². Find the horizontal speed.' Requiring students to match to y = gx²/(2u²) → u = √(g/6).
- y = gx²/(2u²) is the trajectory for horizontal launch — matching coefficients gives u
- AP Physics C tests numerical projectile problems but not coefficient-matching with trajectory equations
- NEET uses trajectory equations to set u and H conditions — a 2-step coefficient identification
NEET-Style Practice Questions — Horizontal Projectile Motion
4 QuestionsPractice Problems — Horizontal Projectile Motion
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Physics — Motion In Two Dimension Revision Checklist
Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.
FAQ — Horizontal Projectile Motion
Notes · Downloads · Revision · Important QuestionsDoes a ball thrown horizontally at higher speed take longer to reach the ground?
What is the shape of the trajectory of a horizontal projectile?
How is the speed at impact calculated for horizontal projectile motion?
How do I find the angle of velocity with the horizontal at impact?
If a ball thrown horizontally and a ball dropped from the same height — which hits the ground first?
How is horizontal projectile motion a special case of oblique projection?
Can the trajectory equation be used to find the height of the launch point?
What is the net velocity of a horizontal projectile at any time t?
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