AQA A-Level Physics Paper 1, June 2024: Question 20

1 mark · Medium difficulty · Multiple Choice

Determine the new range of a projectile fired with double the initial velocity at the same angle.

Practise this question

Question

A multiple-choice question showing a diagram of a projectile trajectory with initial velocity u at angle theta, and a total horizontal range d. A second projectile is fired with velocity 2u at the same angle, and students must choose the correct new range from options A (√2d), B (2d), C (2√2d), and D (4d).
Question text

20 A projectile is fired from ground level over horizontal ground.

Its initial velocity is u at an angle θ to the horizontal.

The range of the projectile is d.

A second projectile is fired with a velocity 2u at the same angle.

What is the range of this projectile?

Assume that air resistance is negligible.

[1 mark]

A 2d

B 2d

C 2 2d

D 4d

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer for question 20 is D, corresponding to a range of 4d.

20 D 4d AO2

How to answer it

Projectile Range Scaling with Initial Velocity

📋 What this question tests

This question assesses your ability to apply kinematic equations to 2D projectile motion, specifically understanding how scaling the initial velocity impacts the horizontal range when launch angles and gravitational field strength remain constant.

Question 20: Multiple Choice Part

Determining the Range of a Scaled Projectile Velocity

✅ Correct Answer

D: 4d

Awarded 1 mark for selecting option D.

💡 Key Knowledge

  • Horizontal motion has no acceleration (velocity is constant): range = horizontal velocity × total time of flight .
  • Vertical motion is governed by constant downward acceleration due to gravity ( g ).
  • Both initial vertical velocity components and time of flight scale linearly with initial velocity u .

🧠 Exam Technique

Instead of doing full derivations from scratch under timed conditions, use proportionality relationships. If initial velocity doubles ( 2u ), how does that feed into the range formula containing squared terms?

❌ Common Errors

A common trap is assuming linear scaling (choosing option B: 2d ) by forgetting that doubling the initial velocity also doubles the time of flight in the air, compounding the effect on the horizontal distance covered.

📐 Step-by-Step Derivation & Calculation

  1. Write out the general range equation: For a projectile launched and landing at the same vertical level, the time of flight t is determined by the vertical motion: t = 2u sin(θ) / g .
  2. Formulate horizontal range ( d ): Range is horizontal velocity multiplied by time of flight:
    d = (u cos(θ)) × (2u sin(θ) / g)
  3. Simplify using trigonometric identities:
    d = (u² / g) × 2 sin(θ) cos(θ) = (u² sin(2θ)) / g
  4. Analyze scaling: Notice that range d is directly proportional to the square of the initial velocity ( d ∝ u² ).
  5. Apply the new velocity: When velocity is doubled to 2u , the new range becomes:
    d_new ∝ (2u)² = 4u² = 4d .

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.