AQA AS Level Physics Paper 2, June 2023: Question 26

1 mark · Medium difficulty · Multiple Choice

Determine the final velocity of a ball dropped from a height of 2h given it hits the ground with velocity v when dropped from height h with negligible air resistance.

Practise this question

Question

Multiple choice question 26. A ball dropped from height h hits the ground with velocity v. When dropped from height 2h with negligible air resistance, what is the impact velocity? Options are A: v, B: sqrt(2)*v, C: v*sqrt(2), D: 2v.
Question text

26 A ball is dropped from a height h. The ball hits the ground with a velocity v.

The ball is now dropped from a height of 2h.

Air resistance is negligible.

What is the velocity at which the ball hits the ground?

[1 mark]

A v

B 2v

C v 2

D 2v

Mark scheme

Show the mark scheme Mark scheme for question 26 indicating the correct answer is C, with the value v multiplied by the square root of 2.

26 C v 2

How to answer it

Velocity in Free Fall Scaling

Question 26 • Multiple Choice • 1 Mark

What this question tests

This question assesses your understanding of kinematic equations of motion under constant acceleration (gravity), specifically how changes in displacement (height) scale non-linearly with final velocity when an object is dropped from rest.

Question Breakdown

✅ Correct Answer: C ( v√2 )

Doubling the drop height h multiplies the final velocity squared by 2, meaning the final velocity is multiplied by the square root of 2 ( √2 ).

💡 Key Knowledge

  • SUVAT equation without time: v² = u² + 2as
  • For an object dropped from rest, initial velocity u = 0 .
  • Acceleration a = g and displacement s = h .
  • Therefore, v² = 2gh .

🧠 Exam Technique

Instead of recalculating with numbers, use proportionality ratios for quick multiple-choice success. Since v ∝ √h , multiplying h by 2 means multiplying v by √2 .

❌ Common Errors

Students frequently fall into the trap of option D ( 2v ), wrongly assuming that doubling the height doubles the final velocity due to a linear relationship.

📐 Step-by-Step Derivation

  1. Initial drop from height h :
    Using v² = 2gh , the initial velocity is given by v = √(2gh) .
  2. Second drop from height 2h :
    Let the new velocity be v' . Using the same equation with new height 2h :
    (v')² = 2g(2h) = 4gh or 2 × (2gh) .
  3. Relate v' to v :
    Taking the square root of both sides gives v' = √(2) × √(2gh) = v√2 .
Examiner Note: This is a classic AQA AS Physics multiple-choice item designed to separate students who memorise formula relationships from those who blindly guess linear scalings. Option C correctly identifies the square-root dependence.

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.