AQA AS Level Physics Paper 2, June 2022: Question 24

1 mark · Medium difficulty · Multiple Choice

Determine the correct comparison of the times of flight and horizontal distances for two balls of different masses projected horizontally from a building when air resistance is not negligible.

Practise this question

Question

Multiple choice question 24 asks to compare the time and horizontal distance of two balls P and Q projected horizontally from a building with air resistance not negligible, where P has a greater mass than Q. A table with four rows (A, B, C, D) presents different combinations of inequalities for time (tp vs tq) and horizontal distance (dp vs dq).
Question text

24 P and Q are two balls of the same diameter. P has a greater mass than Q.

Both balls are projected at the same time from the top of a tall building that stands

on horizontal ground.

Both balls are projected with the same horizontal velocity.

P reaches the ground after time tP and at a horizontal distance dP from the building.

Q reaches the ground after time tQ and at a horizontal distance dQ from the building.

The air is still and air resistance is not negligible.

Which row is correct?

[1 mark]

Time Horizontal distance

A tP = tQ dP = dQ

B tP = tQ dP > dQ

C tP < tQ dP = dQ

D tP < tQ dP > dQ

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer is D, with the corresponding relationships tp < tq and dp > dq.

24 D (AO1) tP < tQ dP > dQ

How to answer it

Projectile Motion with Air Resistance

What this question tests

This question assesses your understanding of projectile motion, specifically how the introduction of non-negligible air resistance affects objects of identical dimensions but different masses. It tests your ability to apply Newton's laws of motion and analyze terminal velocity and deceleration factors in vertical and horizontal directions.

Question 24: Multiple Choice Analysis

Evaluating the Correct Row (D)

✅ Correct Answer: Row D

tP < tQ and dP > dQ

Marks: 1 / 1 (AO1)

💡 Key Knowledge

  • Air resistance depends on speed and cross-sectional area (both balls have the same diameter).
  • Drag force acts upwards against gravity and backwards against horizontal motion.
  • Heavier objects have a higher mass, meaning acceleration is less affected by a given drag force (F = ma, so a = F/m).

🧠 Exam Technique

  • Break the motion down into components: analyze the vertical time of flight first, then look at how horizontal distance is affected.
  • Eliminate options systematically based on standard textbook assumptions vs. the twist in this question ("air resistance is not negligible").

❌ Common Errors

  • Assuming time is equal: Forgetting that air resistance changes the effective downward acceleration. Students often fall back on the standard ideal-physics rule that "horizontal and vertical motions are independent and time depends only on height." That only applies in a vacuum!
  • Confusing mass effects: Thinking lighter objects fall faster due to less inertia. In reality, drag has a proportionally larger decelerating effect on lighter object Q.

Step-by-Step Examiner Breakdown

Step 1: Analyze the Vertical Motion (Time t)

Both balls experience a downward gravitational force and an upward drag force. The net downward force is mg - Drag .

Using Newton's Second Law ( a = (mg - Drag) / m = g - (Drag / m) ):

  • Since P has a greater mass than Q (mP > mQ) and both have the same diameter, they experience roughly similar drag forces at any given speed.
  • Therefore, the term Drag / m is smaller for ball P than for ball Q.
  • Ball P experiences a greater net downward acceleration than ball Q.
  • Greater acceleration means ball P hits the ground sooner: tP < tQ.

Step 2: Analyze the Horizontal Motion (Distance d)

Horizontal distance traveled is given by d = horizontal velocity × time .

  • Both start with the same horizontal velocity.
  • Air resistance creates a horizontal decelerating force on both balls.
  • Because ball P is in the air for a shorter time (tP < tQ), it is subjected to horizontal drag for less time. Furthermore, its larger mass gives it more inertia against horizontal deceleration.
  • Consequently, ball P slows down horizontally less than ball Q and travels further: dP > dQ.

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2022. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.