Projectile Motion – Complete Notes, Revision, Important Questions & Downloads
Projectile motion is two-dimensional motion under gravity alone (no engine force). Five subtopics are covered: Introduction of Projectile Motion (definition and examples), Assumptions of Projectile Motion (no air resistance, negligible Earth curvature/rotation, constant g), Principle of Physical Independence of Motions (horizontal and vertical motions independent), Types of Projectile Motion (oblique, horizontal, inclined plane), and Oblique Projectile Motion (parabolic trajectory, T=2u sinθ/g, R=u²sin2θ/g, H=u²sin²θ/2g). NEET primarily tests the oblique case — range formula, maximum range at 45°, height formula, time of flight, trajectory equation y = x tanθ − gx²/(2u²cos²θ), and complementary angles (same range for θ and 90°−θ). These are direct calculation questions in almost every NEET paper.
NEET Weightage — Projectile Motion
Motion In Two Dimension (Chapter 3)| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2024 | 1 | 4 | |
| 2023 | 2 | 8 | |
| 2022 | 1 | 4 | |
| 2021 | 2 | 8 | |
| 2020 | 1 | 4 | |
| 2019 | 1 | 4 | |
| 6-Year Total (2019–2024) | 6–10 | 24–40 |
The ratio H:R_max = u²sin²θ/(2g) : u²/g = sin²θ/2 → at θ = 45°, H = R_max/4. NEET often asks 'if R = 4H, find projection angle' → θ = 45°.
Trajectory equation y = x tanθ − gx²/(2u²cos²θ) is a parabola. NEET tests the shape (parabolic) and the coefficient identification to extract initial conditions.
How to Prepare Projectile Motion for NEET
Memorise the three primary formulas with derivation logic T = 2u sinθ/g (time for v_y to change from +u sinθ to −u sinθ). H = u²sin²θ/(2g) (v_y = 0 at max height). R = u²sin2θ/g (horizontal distance = u cosθ × T). Each formula derives in 2 lines — knowing the logic prevents sign errors.
Complementary angle pairs — drill this pattern θ and (90°−θ) give the same R but different H and T. At 45°: R is maximum = u²/g. At 45°: H = R_max/4. NEET uses: 'Given range at 30°, find range at 60°' — same range. 'Given range at 40°, find the other angle for same range' → 50°.
Trajectory equation — know the form and parabola y = x tanθ − gx²/(2u²cos²θ). This gives a downward-opening parabola. NEET may give a = coefficient of x², b = coefficient of x and ask for range (R = ab/coefficient relations). Know y = 0 when x = R.
Principle of physical independence — exam trap Horizontal: uniform motion (u_x = u cosθ = constant, no air resistance). Vertical: uniformly accelerated (a_y = g). They are independent — horizontal velocity does not affect time of flight. A key NEET trap: 'A ball dropped and a ball thrown horizontally from the same height hit the ground at the same time' — TRUE because T depends only on vertical component.
Study Materials — Projectile Motion
PDF · Cheat Sheet · MCQ Set · PYQSubtopics in Projectile Motion
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Rapid Revision — Projectile Motion
Concept → Trap → Example1) Introduction of Projectile Motion
CoreA projectile is a body in flight under gravity alone (no engine force). The path is a parabola. Initial velocity has horizontal (u cosθ) and vertical (u sinθ) components. Examples: cricket ball, football, stone thrown at angle.
- The word 'projectile' means propelled body — but after initial projection, only gravity acts on it. No thrust, no air resistance (in NEET).
- The trajectory (path) is a parabola for oblique projection and a straight vertical line for purely vertical projection.
- NEET question: 'A particle is projected at angle θ to horizontal with speed u. Which of the following changes during flight — speed, velocity, acceleration, momentum?' Speed and velocity and momentum change; acceleration = g = constant throughout.
2) Assumptions of Projectile Motion
ConceptualThree assumptions: (1) Air resistance neglected. (2) g is uniform and constant throughout. (3) Earth's curvature neglected (short ranges only).
- Assumption 1 (no air resistance): Enables horizontal velocity to remain constant throughout. Real projectiles (like bullets) slow down due to air drag — NEET assumes ideal case.
- Assumption 2 (constant g): For heights much less than Earth's radius (~6400 km), g ≈ 9.8 m/s² is valid. For ballistic missiles at high altitudes, g varies.
- Assumption 3 (no Earth curvature): For range << Earth radius, the flat-Earth approximation is valid. Affects only very long-range projectiles.
3) Principle of Physical Independence of Motions
High YieldHorizontal and vertical motions are completely independent. Horizontal: uniform (u_x = u cosθ = constant). Vertical: uniformly accelerated (a = g downward). Each can be analysed separately.
- Independence means horizontal velocity does not affect time of flight (vertical motion determines when it lands).
- Classic NEET: A ball thrown horizontally at 10 m/s and another dropped from same height. Both hit the ground at the same time — the horizontal velocity has no effect on T = √(2H/g).
- At maximum height: vertical velocity = 0 (v_y = 0), but horizontal velocity = u cosθ still exists. Speed at max height = u cosθ, NOT zero.
4) Types of Projectile Motion
ConceptualTwo types: (1) Oblique projection: u has both horizontal and vertical components (angle θ with horizontal, 0 < θ < 90°). (2) Horizontal projection: u is purely horizontal (θ = 0°). Vertically upward (θ = 90°) is a special case with no horizontal range.
- Oblique projection: the standard textbook case. Results in a parabolic path. Formulas T = 2u sinθ/g, H = u²sin²θ/(2g), R = u²sin2θ/g apply.
- Horizontal projection: θ = 0°, so T = √(2H/g) (from height H), R = u√(2H/g). This is the 'ball thrown horizontally from a cliff' case.
- NEET distinguishes: if 'horizontal projection', use H and g to get T — not the angle formula. If 'oblique projection at angle θ', use T = 2u sinθ/g.
5) Oblique Projectile Motion
High YieldProjection at angle θ, speed u. Components: u_x = u cosθ, u_y = u sinθ. Time of flight T = 2u sinθ/g. Max height H = u²sin²θ/(2g). Range R = u²sin2θ/g. Trajectory: y = x tanθ − gx²/(2u²cos²θ).
- R is maximum at θ = 45°: R_max = u²/g. At this angle, H = R_max/4 = u²/(4g).
- Complementary angles: same R for θ and (90°−θ). e.g. R(30°) = R(60°) = u²sin60°/g = u²(√3/2)/g.
- Important ratio: H/R = (u²sin²θ/2g)/(u²sin2θ/g) = sin²θ/(2sin2θ) = sinθ/(4cosθ) = tanθ/4. So H = R tanθ/4.
US Curriculum Gaps — Projectile Motion
Topics in this section are tested in NEET but less emphasised in standard US physics courses.Trajectory Equation and Parabola Form (AP Physics 1 Gap)
AP Physics 1 tests projectile motion numerically (time, range, height) but does NOT require derivation or knowledge of the explicit trajectory equation y = x tanθ − gx²/(2u²cos²θ). NEET directly asks students to identify this as a parabola or to use the equation form to find the horizontal range or initial speed. The trajectory equation derivation (eliminate t between x = u cosθ·t and y = u sinθ·t − ½gt²) is standard in Indian NEET textbooks.
- AP Physics 1: kinematics equations applied numerically to projectile problems
- NEET: trajectory equation must be memorised and applied to find shape, range, and conditions
- The H = R tanθ/4 derived relation and proof that trajectory is parabolic are NEET-specific derivations
Complementary Angle Property and Special Ratios (AP Physics C: Mechanics Gap)
AP Physics C: Mechanics covers projectile motion through calculus but does not drill the complementary angle property (θ and 90°−θ give the same range) or the H/R_max = 1/4 relation as explicit exam facts. NEET treats these as high-frequency MCQ patterns. Students must also know: if R(30°) = R(60°), and that at 45° the range is maximum and H = R/4.
- Complementary angle property: sin2θ = sin2(90°−θ) because sin(2θ) = sin(180°−2θ) → same R
- At θ=45°: R_max = u²/g; H = u²/(4g) = R_max/4 — this ratio is a direct NEET question
- The proof that R(θ₁) = R(θ₂) iff θ₁ + θ₂ = 90° is not in standard AP curriculum
NEET-Style Practice Questions — Projectile Motion
4 QuestionsPractice Problems — 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 — Projectile Motion
Notes · Downloads · Revision · Important QuestionsIs the speed zero at the highest point of a projectile's trajectory?
Why do two bodies thrown at 30° and 60° have the same range?
What is the angle for maximum range, and what is its value?
How do we derive the trajectory equation (the parabola)?
At what angle is the range equal to the maximum height?
What is the acceleration at the highest point of a projectile?
What is the velocity at angle with horizontal at any time t?
How does the horizontal velocity change during projectile motion?
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