Moderate -0.8 This is a straightforward application of a single SUVAT equation (vĀ² = uĀ² + 2as) with u=0, requiring simple algebraic rearrangement to reach the given inequality. The 3-mark allocation reflects routine substitution and manipulation rather than problem-solving, making it easier than average for A-level.
A ball is released from rest from a height \(h\) metres above horizontal ground and falls freely downwards.
When the ball reaches the ground, its speed is \(v\) m s\(^{-1}\), where \(v \leq 10\)
Show that
$$h \leq \frac{50}{g}$$
[3 marks]
Question 14:
14 | Identifies consistent values for
u, a and s
Do not condone numerical value
of unless recovered later.
PI
šØšØ | 3.4 | B1 | , and
š¢š¢ = 0 š£š£ = 10, šš = šØšØ š š = ā
v2 ā¤ 100
2
100 ā„ 0 +2šØšØā
g2h ā¤ 100
50
ā ā¤
šØšØ
Selects appropriate constant
acceleration equation and
substitutes their values of u, a
and s, allow numerical value of
here (accept equality or
inequality at this stage). šØšØ
Condone v2 not substituted for. | 1.1a | M1
Completes reasoned argument
to justify the given inequality.
AG | 2.1 | R1
Question 14 Total | 3
Q | Marking instructions | AO | Marks | Typical solution
A ball is released from rest from a height $h$ metres above horizontal ground and falls freely downwards.
When the ball reaches the ground, its speed is $v$ m s$^{-1}$, where $v \leq 10$
Show that
$$h \leq \frac{50}{g}$$
[3 marks]
\hfill \mbox{\textit{AQA AS Paper 1 2022 Q14 [3]}}