Falling with air resistance

Key idea: H2 Physics lessons on weight, projectile components, gravitational potential energy, air resistance and terminal velocity.

  • GCE A-Level H2 Physics 2027

Learn the idea

Big question: Why does a falling object stop accelerating even though it keeps moving?

Weight is nearly constant while air resistance grows with speed. The downward resultant therefore decreases, so speed still rises but at a decreasing rate. At terminal velocity drag equals weight: acceleration is zero and kinetic energy is constant, yet gravitational potential energy continues to decrease and is transferred thermally.

Follow the changing force balance

Just after release, drag is small and weight gives a large downward resultant. As speed rises, drag grows, so the resultant and acceleration shrink even though the object is still speeding up.

At terminal velocity, drag equals weight. The forces have not disappeared: their vector sum is zero, so acceleration is zero and velocity is constant.

Check your understanding: If acceleration is decreasing during a fall, must speed be decreasing?

No. Speed still increases while acceleration is downward; it simply increases more slowly.

Track all energy transfers

Before terminal speed, falling reduces gravitational potential energy. Part increases kinetic energy and part is transferred to internal-energy stores by drag.

At terminal speed, kinetic energy is constant, but height continues to fall. The continuing gravitational-store decrease is therefore transferred entirely to internal-energy stores of the air, object and surroundings.

Check your understanding: At terminal speed, is power transferred by drag zero?

No. Drag acts while the object moves, so it continues to transfer energy thermally even though net force is zero.

Ideal projectile trajectory compared with motion under air resistanceTwo trajectories start with the same velocity. The ideal trajectory is higher, longer and symmetric. With drag, the trajectory is lower, shorter and asymmetric. A drag arrow points opposite to the velocity on the descending path.velocitydrag opposes velocityideal: no air resistancewith air resistance
Scroll diagram horizontally to read all labels.
For the same launch conditions and equal launch and landing heights, drag reduces maximum height and range and breaks the ideal trajectory's symmetry.

Key ideas to keep

  • Terminal velocity means balanced forces, not no forces.
  • Zero acceleration can accompany a non-zero constant velocity.
  • Drag always opposes the instantaneous motion.

Worked example

Connect a measured acceleration to drag

Question: A 75 kg skydiver is falling downward at 30 m s⁻¹ with downward acceleration 2.0 m s⁻². Find the drag force and the rate at which drag transfers energy to internal stores. Use g = 9.81 m s⁻².

  1. Step 1: Write the downward resultant

    Why: Weight and drag oppose each other.

    Working: mg − D = ma, so D = m(g − a) = 75(9.81 − 2.0) = 585.75 N.

  2. Step 2: Find drag power

    Why: Drag is opposite velocity, so its magnitude times speed is the rate of thermal transfer.

    Working: Pdrag = Dv = 585.75(30) = 1.76 × 10⁴ W.

  3. Step 3: Interpret the remainder

    Why: Not all gravitational power becomes heating while speed is still rising.

    Working: Gravity transfers mgv = 2.21 × 10⁴ W; the difference 4.50 kW increases kinetic energy.

Answer: Drag is about 586 N upward and transfers energy thermally at about 17.6 kW.

Check: Drag is below the 736 N weight, so a downward resultant and increasing speed are consistent.

Question

A skydiver falls from rest, reaches terminal velocity, opens a parachute and later reaches a lower terminal velocity. Explain the complete force and energy sequence.

Check the worked solution

Before the first terminal speed, weight exceeds drag and speed rises; increasing drag reduces acceleration. At terminal speed drag equals weight. Opening the parachute makes drag exceed weight, so the upward resultant slows the downward motion and kinetic energy falls while energy is transferred thermally. As speed falls, drag falls until it again equals weight at a lower constant speed.

Practise with support

Try this

An 80 kg skydiver falls at a terminal speed of 50 m s⁻¹. Use g = 9.8 N kg⁻¹. Find drag and the rate at which gravitational potential energy is transferred.

Hint: At terminal speed the forces balance, but the downward displacement continues.

Check your answer

Drag = weight = mg = 784 N upward. The gravitational potential-energy loss rate is mgv = 784(50) = 39.2 kW, transferred mainly to thermal stores by drag.

Practise independently

Your turn

Describe force, acceleration, kinetic-energy change and energy transfers immediately before and after a falling parachutist opens a parachute, and at the new terminal velocity.

Check your answer

Before opening at the first terminal speed, drag equals weight and kinetic energy is constant. Immediately after opening, drag exceeds weight, the resultant and acceleration are upward, and the downward speed and kinetic energy decrease while energy is transferred thermally. At the new lower terminal speed, drag again equals weight; kinetic energy is constant while gravitational potential energy continues to be dissipated.

Common mistakes

Common mistake

At terminal velocity no forces act and no energy is transferred.

What is wrong with this reasoning?

Show better thinking

Weight and drag both act but balance. Speed and kinetic energy stay constant while gravitational potential energy continues to be transferred to thermal stores in the object, air and surroundings.

Exam guidance

Describe release, approach to terminal speed and terminal motion as three distinct stages.

Exam-style practice [7 marks]

Describe a raindrop's motion and energy transfers from release until long after it reaches terminal velocity. Your answer must refer to weight, drag, resultant force, acceleration, speed and energy stores.

Plan before you answer

  • Describe release, approach and terminal stages.
  • Keep acceleration and speed distinct.
  • Continue the energy account after kinetic energy becomes constant.
Mark your answer and compare the model

Marking points

Tick each point only if your answer states it clearly.

Model answer

At release, drag is nearly zero, so weight gives a large downward resultant and the drop accelerates. As speed rises, drag rises, reducing the resultant and acceleration; speed still rises but more slowly. When drag equals weight, resultant force and acceleration are zero, so terminal speed is constant. Before then, decreasing gravitational potential energy becomes both kinetic energy and internal energy. At terminal speed the kinetic store is constant, but gravitational potential energy continues to decrease and is transferred to internal-energy stores by drag.

Check what stayed with you

Recall question 1

What condition defines terminal velocity?

Check the answer

Drag equals weight, so resultant force and acceleration are zero.

Recall question 2

What happens to kinetic energy at terminal speed?

Check the answer

It stays constant.

Recall question 3

Why does gravitational potential energy still decrease?

Check the answer

The object continues moving downward and losing height.

Try this next

Use the longer mixed questions to connect the ideas, calculations and diagrams from this topic.

Open Projectile Motion quiz

Syllabus and review details

This lesson covers the listed H2 Physics 9478 outcomes. Treat horizontal and vertical motion separately, then connect them through their shared time. In the ideal model, air resistance is negligible and gravitational acceleration is uniform; questions about drag must state that a resistive force is present.

  • GCE A-Level H2 PhysicsTopic 5(e) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027