Hint

Choose and retain a positive direction; distinguish signed quantities from magnitudes. Use the two-body pulley model only before the floor event.

Worked solution

(a)

Use the two-body pulley model only before the floor event.

The taut-stage mass difference divided by total mass, times g, gives \(5\) \(\displaystyle \frac{m}{s^{2}}\).

Answer: \(5\) \(\displaystyle \frac{m}{s^{2}}\)

(b)

Use the shared first-stage displacement and the positive speed root.

The lighter moves the same distance \(\displaystyle \frac{8}{5}\) m; \(\displaystyle v^{2}\)=2ah=16, so its speed is \(\displaystyle \frac{4m}{s}\).

Answer: \(4\) m/s

(c)

Use gravity alone after the constraint is lost.

In free upward motion, \(\displaystyle 0=V^{2}-20s\) gives \(\displaystyle \frac{4}{5}\) m.

Answer: \(\displaystyle \frac{4}{5}\) m

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-body pulley model only before the floor event.
• 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: Do not keep the old tension in a stage where the string is slack.

(b) · 2 marks

• 1 mark: Use the shared first-stage displacement and the positive speed root.
• 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: Transfer the event velocity to the new stage, but reset that stage’s time.

(c) · 2 marks

• 1 mark: Use gravity alone after the constraint is lost.
• 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: Do not keep the old tension in a stage where the string is slack.

Total: 6 marks.