Falling with air resistance
Key idea: H2 Physics lessons on weight, projectile components, gravitational potential energy, air resistance and terminal velocity.
Continue where you stopped
The core idea
Build the idea
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.
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.
See the reasoning
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.
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.
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.
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.
Another worked model
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.
Use a hint if needed
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.
Now work without the hint
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.
Avoid these traps
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.
Write for the examiner
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.
Come back in three days
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.
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