Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Use the two perpendicular resultant components.
Worked solution
(a)
Use the two perpendicular resultant components.
Pythagoras gives \(12.7\) N.
Answer: \(12.7\) N
(b)
Negate the horizontal component of the resultant.
The balancing horizontal component must be -9 N.
Answer: \(-9\) N
(c)
Use inverse tangent and identify the first-quadrant resultant.
The positive component ratio is \(1\), giving 45.0°.
Answer: \(45.0\)°
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Use the two perpendicular resultant components.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and required final precision is acceptable.
Common error: The equilibrant reverses the entire resultant, not only one component.
(b) · 2 marks
- 1 mark: Negate the horizontal component of the resultant.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Use a degree-mode inverse tangent with the correct component order.
(c) · 2 marks
- 1 mark: Use inverse tangent and identify the first-quadrant resultant.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and required final precision is acceptable.
Common error: The equilibrant reverses the entire resultant, not only one component.
Total: 6 marks.