A Level · AS · structured
AS Level foundations · Question 7
AS Level foundations · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 14
- Topics
- 3
- Answer
- Complete
A skydiver of total mass 85 kg falls from rest from a stationary balloon. The drag force F on the skydiver is related to her speed v by F = kv², where k is a constant. She reaches a terminal velocity of 55 m s⁻¹ before opening her parachute.
- (a)
State State what is meant by terminal velocity.
2 marks - (b)
Explain Explain, with reference to Newton's laws, why the acceleration of the skydiver decreases as her speed increases.
3 marks - (c)
Determine Determine the value of k, and state its SI base units.
3 marks - (d)
Calculate Calculate the acceleration of the skydiver at the instant when her speed is 30 m s⁻¹.
3 marks - (e)
Explain The skydiver opens her parachute while travelling at the terminal velocity of 55 m s⁻¹. Explain what happens to her motion immediately afterwards, and describe the new terminal velocity she reaches.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
State State what is meant by terminal velocity.
Answer the command word directly and use precise physical vocabulary. Include only the distinct features or facts that earn marks, without burying them in unrelated background information.
- 1
the constant (maximum) velocity reached by a falling body
- 2
when the drag force has grown to equal the weight, so the resultant force and the acceleration are zero
(b)
Explain Explain, with reference to Newton's laws, why the acceleration of the skydiver decreases as her speed increases.
State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.
- 1
the weight is constant, but the drag force increases as the speed increases
- 2
so the resultant force, weight minus drag, decreases
- 3
and by Newton's second law a = F/m, so the acceleration decreases while the speed still increases
(c)
Determine Determine the value of k, and state its SI base units.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
at terminal velocity, kv² = mg, so k = 85 × 9.81 / 55²
- 2
Substituting the terminal values into k = mg/v² gives k = 0.276.
- 3
From k = F/v², the SI base units of k are kg m⁻¹.
(d)
Calculate Calculate the acceleration of the skydiver at the instant when her speed is 30 m s⁻¹.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
drag F = 0.276 × 30² = 248 N
- 2
resultant = 834 − 248 = 586 N
- 3
a = 586 / 85 = 6.9 m s⁻²
(e)
Explain The skydiver opens her parachute while travelling at the terminal velocity of 55 m s⁻¹. Explain what happens to her motion immediately afterwards, and describe the new terminal velocity she reaches.
State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.
- 1
opening the parachute increases k sharply, so at 55 m s⁻¹ the drag now greatly exceeds the weight
- 2
the resultant force acts upwards, so she decelerates
- 3
the drag falls as she slows until it again equals the weight, giving a new, much lower terminal velocity
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