Moderate -0.8 This is a straightforward SUVAT kinematics problem requiring application of s = ut + ½at² twice and subtraction. The setup is clear, the method is standard, and 'show that' questions provide a target to work towards, making it easier than average but not trivial due to the two-step calculation and unit conversion.
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]
Question 16:
16 | Forms correct constant
acceleration equation for
displacement with t = 0.5 for first
apple
Condone 0 not shown for u | 1.1b | B1 | 1
s =0+ (9.8)(0.5)2=1.225 m
1
2
1
s =0+ (9.8)(0.6)2= 1.764 m
2
2
s −s =0.539 m
2 1
d =53.9cm
So
d ≈54cm
Forms constant acceleration
equation for displacement with
t = 0.6 for second apple
Condone 0 not shown for u | 3.1b | M1
Finds the difference in heights
between the two apples | 1.1a | M1
Completes reasoned argument
to show d is approximately 54
Must see 53.9 or 0.539
Condone d = 54
AG | 2.1 | R1
Question 16 Total | 4
Q | Marking Instructions | AO | Marks | Typical Solution
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]
\hfill \mbox{\textit{AQA Paper 2 2024 Q16 [4]}}