Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Use cosine for the component along the axis from which α is measured.
Worked solution
(a)
Use cosine for the component along the axis from which α is measured.
\(\displaystyle F \cos \alpha =\)\(\displaystyle \frac{124}{5}\) N.
Answer: \(\displaystyle \frac{124}{5}\) N
(b)
Use sine for the component perpendicular to the reference horizontal.
\(\displaystyle F \sin \alpha =\)\(\displaystyle \frac{93}{5}\) N.
Answer: \(\displaystyle \frac{93}{5}\) N
(c)
Subtract the leftward force from the horizontal component, then use Pythagoras.
The resultant components are \(\displaystyle \frac{104}{5}\) and \(\displaystyle \frac{93}{5}\) N. Pythagoras gives \(27.9\) N.
Answer: \(27.9\) N
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 cosine for the component along the axis from which α is measured.
- 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: Check which axis the supplied angle is measured from.
(b) · 2 marks
- 1 mark: Use sine for the component perpendicular to the reference horizontal.
- 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: Find the resultant components before its magnitude and direction.
(c) · 2 marks
- 1 mark: Subtract the leftward force from the horizontal component, then use Pythagoras.
- 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: Check which axis the supplied angle is measured from.
Total: 6 marks.