June 2024 Paper 2 Q16
16 In this question use \(g = 9.8\) m s−2
An apple tree stands on horizontal ground.
An apple hangs, at rest, from a branch of the tree.
A second apple also hangs, at rest, from a different branch of the tree.
The vertical distance between the two apples is \(d\) centimetres.
At the same instant both apples begin to fall freely under gravity.
The first apple hits the ground after 0.5 seconds.
The second apple hits the ground 0.1 seconds later.
Show that \(d\) is approximately 54 [4 marks]
| Scheme | Marks | AO |
|---|---|---|
| Forms correct constant acceleration equation for displacement with \(t\) = 0.5 for first apple Condone 0 not shown for \(u\) | B1 | 1.1b |
| Forms constant acceleration equation for displacement with \(t\) = 0.6 for second apple Condone 0 not shown for \(u\) | M1 | 3.1b |
| Finds the difference in heights between the two apples | M1 | 1.1a |
| Completes reasoned argument to show \(d\) is approximately 54 Must see 53.9 or 0.539 Condone \(d\) = 54 AG | R1 | 2.1 |
| (4 marks) |
Typical solution
\[s_1 = 0 + \frac{1}{2}(9.8)(0.5)^2 = 1.225\text{ m}\]\[s_2 = 0 + \frac{1}{2}(9.8)(0.6)^2 = 1.764\text{ m}\]\[s_2 - s_1 = 0.539\text{ m}\]\[d = 53.9\text{ cm}\]So
\[d \approx 54\text{ cm}\]