Theme A — Space, Time and Motion
A.1.6 Projectile Motion — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 8 of 63 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
A.1.6 Projectile Motion — IB PHYSICS SL notes: Analyse projectile motion by treating horizontal and vertical components independently, with and without air resistance.Projectile = a particle moving freely under gravity alone in a two-dimensional plane, after being launched.Exampl…
- Assumptions
- Independence
- Components of the launch velocity
- Vertical (up positive)
- Horizontal launch from height h
- Landing speed
Section 1 of 9What a projectile is
Projectile
Projectile a particle moving freely under gravity alone in a two-dimensional plane, after being launched.
- Examples are a thrown ball, a diver leaving a board and a struck baseball.
Assumptions
- Assumptions fluid resistance is negligible and g is constant near Earth's surface.
Launch
- Launch speed u at an angle θ to the horizontal.
Section 2 of 9Horizontal and vertical components
Horizontal and vertical components
Independence
- Independence the horizontal and vertical motions are independent of each other and are analysed separately with the suvat equations.
Time
- Time it is the same for both directions and is the link between them.
Components of the launch velocity
- Components of the launch velocity horizontal u cos θ and vertical u sin θ.
| Quantity | Horizontal | Vertical |
|---|---|---|
| Acceleration | Zero | g = 9.8 m s−2 downwards |
| Velocity | Constant | Changes uniformly; zero at maximum height |
| Displacement | Range at the end of the flight | Maximum height at half the flight time |
Section 3 of 9Equations of motion
1Horizontal
- Horizontal ax = 0, so x = uxt with ux constant.
2Vertical (up positive)
- Vertical (up positive) vy = uy − gt, y = uyt − ½gt2 and vy2 = uy2 − 2gy.
3Horizontal launch from height h
- Horizontal launch from height h uy = 0 so the fall time is t = √(2h/g), independent of the horizontal speed.
- A ball dropped and a ball fired horizontally from the same height reach level ground together.
4Landing speed
- Landing speed v = √(vx2 + vy2) at angle tan−1(vy / vx) below the horizontal.
Section 4 of 9Level-ground results
Path
- Path a symmetric parabola when launch and landing heights are equal.
Highest point
- Highest point vy = 0 but the speed equals vx, which is not zero.
Time of flight
- Time of flight the time to the top is uy/g, so the total time is 2uy/g.
Maximum height
- H = uy2 / (2g).
Range
- R = u2 sin 2θ / g, greatest at θ = 45°.
- Complementary angles such as 30° and 60° give the same range.
- The steeper angle has the longer flight time and greater height.
Acceleration
- Acceleration it is 9.8 m s−2 downwards at every point and the velocity is tangent to the path.
Section 5 of 9Effect of air resistance
Without drag
- Without drag mechanical energy is conserved, so the speed at a given height does not depend on the launch angle.
With drag
- With drag the resistive force opposes the velocity and the path is no longer a parabola.
| Quantity | Effect of air resistance |
|---|---|
| Time of flight | Decreases |
| Horizontal velocity | Decreases |
| Range | Decreases |
| Maximum height | Decreases |
| Trajectory | Steeper on the way down than on the way up |
| Landing speed | Lower |
- Light objects
- a badminton shuttle is affected far more than a dense shot put, because the force depends on speed and cross-section.
Section 6 of 9Method and applications
1
Resolve the launch velocity into horizontal and vertical components.
2
Choose signs and list the known values for each direction.
3
Use the vertical equations to find the time.
4
Use x = uxt with that time to find the range.
5
Combine components if the final speed or direction is wanted.
Method and applications
Quadratic in t
- Quadratic in t it appears when there is a height difference between launch and landing.
Sport
- Sport a shot putter releases above ground level, so the best angle is a little below 45°.
Gymnastics and ski jumping
- Gymnastics and ski jumping a large initial vertical velocity gives greater height and flight time.
Section 7 of 9More from the specification
More from the specification
Projectile motion
- Projectile motion horizontal velocity is constant while vertical motion has constant acceleration g downward.
Independence of components
- Independence of components the two motions are analysed separately and share only the time of flight.
Motion graphs
- Motion graphs the gradient of a displacement-time graph gives velocity and of a velocity-time graph gives acceleration.
Terminal velocity
- Terminal velocity a skydiver or cyclist stops accelerating when drag equals the driving or weight force.
Average speed
- Average speed total distance divided by total time; area under a velocity-time graph gives displacement.
Distance
- Total length of path travelled, a scalar.
Terminal
- Connection point of a cell, labelled + or −.
Gradient
- Slope of a graph line.
Vector
- Quantity with magnitude and direction.
Terminal velocity
- Constant speed when air resistance equals weight.
Kinematic equations
- Equations relating displacement, velocity, acceleration and time for constant acceleration.
Velocity-time graph
- A graph of velocity against time whose gradient is acceleration and area is displacement.
Average speed
- Total distance divided by total time.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Projectile | Object moving under gravity alone after launch |
| Trajectory | The curved path followed by a projectile |
| Component | Part of a vector along a chosen axis |
| Time of flight | Total time from launch to landing |
| Range | Horizontal distance travelled before landing |
| Parabola | Shape of the path when air resistance is negligible |
Section 9 of 9Exam technique
1
Thinking the horizontal velocity changes because gravity acts — without drag it is constant.
2
Believing the speed is zero at the top — only the vertical component is zero.
3
Using the launch speed in the suvat equations instead of its components — resolve first.
4
Assuming a heavier object falls faster — without air resistance all fall together.
5
Drawing the real path with drag as symmetric — it is steeper on the way down.
Marked practiceQuizzes for this lesson
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Physics 0625 & 9702 SUVAT Mastery
Graph Interpretation
Constant Acceleration Equations (SUVAT) & Slopes
v = u + at | s = ut + ½at2 | v2 = u2 + 2as | s = ½(u + v)t
- Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
- Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
- Free Fall in vacuum:
a = g ≈ 9.81 m/s2downwards (air resistance negligible).