Projectiles — A-Level Mathematics Revision
Revise Projectiles for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Quantities & Units in MechanicsWhat is Projectiles?
Projectiles at A-Level involves analysing the motion of an object that is thrown or projected into the air. You will learn to model the motion of a projectile using vectors and the constant acceleration equations, and to find quantities such as the time of flight, range, and maximum height.
Board notes: All A-Level Maths boards (AQA, Edexcel, OCR) cover projectiles in their mechanics content. The complexity of the problems, such as those involving projectiles landing on a different level, is similar across the boards.
Step-by-step explanationWorked example
A ball is thrown with an initial speed of 20 m/s at an angle of 30° to the horizontal. What is the maximum height reached by the ball? The initial vertical velocity is 20*sin(30°) = 10 m/s. At the maximum height, the vertical velocity is 0. Using the suvat equation v² = u² + 2as, we have 0² = 10² + 2*(-9.8)*s. This gives 19.6s = 100, so s = 100/19.6 = 5.10 m (to 3 s.f.).
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Common mistakes
- 1Confusing the horizontal and vertical components of the motion. The horizontal motion has constant velocity, while the vertical motion has constant acceleration due to gravity.
- 2Making sign errors with the acceleration due to gravity. It is usually taken as -9.8 m/s², but it is important to be consistent with the chosen positive direction.
- 3Incorrectly using the trigonometric functions to find the initial horizontal and vertical components of the velocity. The horizontal component is v*cos(θ) and the vertical component is v*sin(θ), where v is the initial speed and θ is the angle of projection.
Projectiles exam questions
Exam-style questions for Projectiles with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Projectiles
Core concept
Projectiles at A-Level involves analysing the motion of an object that is thrown or projected into the air. You will learn to model the motion of a projectile using vectors and the constant accelerati…
Frequently asked questions
How do you find the range of a projectile?
The range of a projectile is the horizontal distance it travels before it returns to its initial height. You can find the range by first finding the time of flight, and then multiplying this by the horizontal component of the velocity.
What is the time of flight of a projectile?
The time of flight is the total time the projectile is in the air. You can find the time of flight by considering the vertical motion and finding the time it takes for the projectile to return to its initial height.