Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Apply Newton’s second law along the east axis.
Worked solution
(a)
Apply Newton’s second law along the east axis.
Eastward force divided by mass gives \(1\) \(\displaystyle \frac{m}{s^{2}}\).
Answer: \(1\) \(\displaystyle \frac{m}{s^{2}}\)
(b)
Apply Newton’s second law along the perpendicular north axis.
Northward force divided by mass gives \(\displaystyle \frac{4}{9}\) \(\displaystyle \frac{m}{s^{2}}\).
Answer: \(\displaystyle \frac{4}{9}\) \(\displaystyle \frac{m}{s^{2}}\)
(c)
Combine perpendicular acceleration components after dividing by mass.
Pythagoras on the acceleration components gives \(1.09\) \(\displaystyle \frac{m}{s^{2}}\).
Answer: \(1.09\) \(\displaystyle \frac{m}{s^{2}}\)
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: Apply Newton’s second law along the east axis.
- 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: Acceleration follows the resultant force, not necessarily either individual force.
(b) · 2 marks
- 1 mark: Apply Newton’s second law along the perpendicular north axis.
- 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 the same mass for both component equations.
(c) · 2 marks
- 1 mark: Combine perpendicular acceleration components after dividing by mass.
- 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: Acceleration follows the resultant force, not necessarily either individual force.
Total: 6 marks.