Easy -1.8 This is a straightforward application of conservation of momentum in 2D with equal masses that coalesce. The calculation is trivial: add the two velocity vectors and divide by 2. It's a 1-mark multiple-choice question requiring only direct recall of the coalescence formula with no problem-solving, making it significantly easier than average A-level questions.
2 Two particles of equal mass are moving on a horizontal surface when they collide.
Immediately before the collision, their velocities are \(\left[ \begin{array} { l } 2 \\ 4 \end{array} \right] \mathrm { ms } ^ { - 1 }\) and \(\left[ \begin{array} { c } 6 \\ - 2 \end{array} \right] \mathrm { ms } ^ { - 1 }\)
As a result of the collision the particles coalesce to become a single particle.
Find the velocity of the single particle, immediately after the collision.
Circle your answer. [0pt]
[1 mark]
\(\left[ \begin{array} { l } 4 \\ 1 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }\)
\(\left[ \begin{array} { l } 4 \\ 3 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }\)
\(\left[ \begin{array} { l } 8 \\ 2 \end{array} \right] \mathrm { ms } ^ { - 1 }\)
\(\left[ \begin{array} { l } 8 \\ 6 \end{array} \right] \mathrm { ms } ^ { - 1 }\)
2 Two particles of equal mass are moving on a horizontal surface when they collide.\\
Immediately before the collision, their velocities are $\left[ \begin{array} { l } 2 \\ 4 \end{array} \right] \mathrm { ms } ^ { - 1 }$ and $\left[ \begin{array} { c } 6 \\ - 2 \end{array} \right] \mathrm { ms } ^ { - 1 }$\\
As a result of the collision the particles coalesce to become a single particle.\\
Find the velocity of the single particle, immediately after the collision.\\
Circle your answer.\\[0pt]
[1 mark]\\
$\left[ \begin{array} { l } 4 \\ 1 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$\\
$\left[ \begin{array} { l } 4 \\ 3 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$\\
$\left[ \begin{array} { l } 8 \\ 2 \end{array} \right] \mathrm { ms } ^ { - 1 }$\\
$\left[ \begin{array} { l } 8 \\ 6 \end{array} \right] \mathrm { ms } ^ { - 1 }$
\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics 2022 Q2 [1]}}