A ball is thrown vertically upward and rises to a maximum height before falling back down. Air resistance acts on the ball throughout its motion. Explain why the speed of the ball when it returns to its original launch height is less than its initial launch speed.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (4 marks)
Air resistance exerts a force opposite to the direction of motion, so it does work against the ball’s displacement.
On the upward journey the force of air resistance removes kinetic energy, converting it into heat.
On the downward journey the same force again removes kinetic energy, so the work done by air resistance is negative for both legs of the trip.
Because the total mechanical energy (kinetic + gravitational potential) decreases, the kinetic energy – and therefore the speed – of the ball when it returns to the launch height is less than the initial launch speed.
On the upward journey the force of air resistance removes kinetic energy, converting it into heat.
On the downward journey the same force again removes kinetic energy, so the work done by air resistance is negative for both legs of the trip.
Because the total mechanical energy (kinetic + gravitational potential) decreases, the kinetic energy – and therefore the speed – of the ball when it returns to the launch height is less than the initial launch speed.
Examiner tips
- Show the direction of the air‑resistance force and state that its work is negative.
- Explain that the loss of mechanical energy occurs over the whole round‑trip.
- Mention that gravitational potential energy is the same at the launch height on both passes.
- Link the reduced kinetic energy to the lower speed on return.
Common mistakes
- Confusing air resistance with gravity or omitting that the work is negative.
- Failing to recognise that the loss of energy happens on both upward and downward legs.
- Assuming the ball returns with the same speed because the height is the same, ignoring energy loss.
Mark scheme (4 marks)
- Air resistance does work against the motion / air resistance exerts a force opposing the direction of displacement
- Air resistance does negative work on the ball / the work done by air resistance is negative (on both the upward and downward journeys)
- The total mechanical energy of the ball decreases / kinetic energy plus gravitational potential energy decreases over the full journey
- Since gravitational potential energy is the same at the original launch height on both journeys, the reduced total mechanical energy means the kinetic energy (and therefore speed) on return is less than at launch
Key terms in this question
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →