Moderate -0.3 This is a straightforward application of conservation of energy (PE + KE) where mass cancels out. The proof requires setting up energy equations and showing the mass term factors out, which is a standard mechanics exercise. However, it does require understanding of energy principles and clear communication of assumptions (no air resistance), making it slightly easier than average but not trivial.
4 A cricket ball of mass 156 grams is thrown from a point which is 1.5 metres above the ground, with a speed of \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
A tennis ball of mass 58 grams is thrown from the same point, with the same speed.
Prove that both balls hit the ground with the same speed.
Clearly state any assumptions you have made and how you have used them. [0pt]
[5 marks]
\(\frac{1}{2}v^2 = \frac{1}{2} \times 12^2 + g \times 1.5\)
\(v^2 = 144 + 3g\)
Answer
Marks
Guidance
\(v = \sqrt{144 + 3g}\)
M1
Uses KE and PE equations correctly for one ball
Hence \(v\) is independent of \(m\) so both balls hit ground with same speed
M1, R1
Forms energy equation and manipulates to find \(v\); completes rigorous argument using energy considerations — \(v\) is independent of mass AG
## Question 4:
Assuming no external forces act, conservation of energy may be applied. Both balls modelled as particles so vertical distance moved is the same. | R1, B1 | Assumes no external forces; assumes balls are particles of same size moving through same vertical distance
$\frac{1}{2}mv^2 = \frac{1}{2}m \times 12^2 + mg \times 1.5$
$\frac{1}{2}v^2 = \frac{1}{2} \times 12^2 + g \times 1.5$
$v^2 = 144 + 3g$
$v = \sqrt{144 + 3g}$ | M1 | Uses KE and PE equations correctly for one ball
Hence $v$ is independent of $m$ so both balls hit ground with same speed | M1, R1 | Forms energy equation and manipulates to find $v$; completes rigorous argument using energy considerations — $v$ is independent of mass **AG**
4 A cricket ball of mass 156 grams is thrown from a point which is 1.5 metres above the ground, with a speed of $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
A tennis ball of mass 58 grams is thrown from the same point, with the same speed.\\
Prove that both balls hit the ground with the same speed.\\
Clearly state any assumptions you have made and how you have used them.\\[0pt]
[5 marks]\\
\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics Q4 [5]}}