Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Multiply mass by signed velocity.
Worked solution
(a)
Multiply mass by signed velocity.
A has velocity \(\displaystyle - \frac{11m}{s}\), giving momentum \(\displaystyle - \frac{77\mathrm{kg}m}{s}\).
Answer: \(-77\) \(\displaystyle \frac{\mathrm{kg}m}{s}\)
(b)
Use the common positive direction for the other particle.
B’s rightward velocity gives \(\displaystyle \frac{18\mathrm{kg}m}{s}\).
Answer: \(18\) \(\displaystyle \frac{\mathrm{kg}m}{s}\)
(c)
Add signed momenta rather than their magnitudes.
The algebraic sum is \(\displaystyle - 77+ 18= - \frac{59\mathrm{kg}m}{s}\).
Answer: \(-59\) \(\displaystyle \frac{\mathrm{kg}m}{s}\)
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: Multiply mass by signed velocity.
- 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: Oppositely directed momenta must have opposite signs.
(b) · 2 marks
- 1 mark: Use the common positive direction for the other particle.
- 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: Zero total momentum does not imply that every particle is at rest.
(c) · 2 marks
- 1 mark: Add signed momenta rather than their magnitudes.
- 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: Oppositely directed momenta must have opposite signs.
Total: 6 marks.