Cambridge International AS & A Level · 1 · structured
Add, subtract and resolve planar vectors
Add, subtract and resolve planar vectors · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 10
- Topics
- 3
- Answer
- Complete
Use east as +x and north as +y. Force A has components (8.0,6.0) N and force B has components (3.0,−4.0) N.
- (a)
Distinguish a scalar from a vector. Classify distance, displacement, speed, velocity, energy and force, giving a reason.
3 marks - (b)
Find A+B and A−B, giving their components and magnitudes. Use a head-to-tail construction or describe the reversal needed for subtraction.
4 marks - (c)
A third force is 12.0 N at 30.0° north of east. Resolve it into east and north components and name which trigonometric function applies to each.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Distinguish a scalar from a vector. Classify distance, displacement, speed, velocity, energy and force, giving a reason.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
State magnitude-only versus magnitude-and-direction distinction.
- 2
Classify all six quantities accordingly.
(b)
Find A+B and A−B, giving their components and magnitudes. Use a head-to-tail construction or describe the reversal needed for subtraction.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
Add components separately:8+3 and6−4.
- 2
Subtract components:8−3 and6−(−4).
- 3
Use Pythagoras for each magnitude.
- 4
Reverse B's direction before adding in the graphical subtraction.
(c)
A third force is 12.0 N at 30.0° north of east. Resolve it into east and north components and name which trigonometric function applies to each.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
The east component is adjacent to the stated angle; use cosine.
- 2
The north component is opposite; use sine.
- 3
Keep both components positive for this direction.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- (a) State magnitude-only versus magnitude-and-direction distinction.
- (a) Classify all six quantities accordingly.
- (b) Add components separately:8+3 and6−4.
- (b) Subtract components:8−3 and6−(−4).
- (b) Use Pythagoras for each magnitude.
- (b) Reverse B's direction before adding in the graphical subtraction.
- (c) The east component is adjacent to the stated angle; use cosine.
- (c) The north component is opposite; use sine.
- (c) Keep both components positive for this direction.
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