AQA M1 2012 January — Question 1 3 marks

Exam BoardAQA
ModuleM1 (Mechanics 1)
Year2012
SessionJanuary
Marks3
PaperDownload PDF ↗
TopicMomentum and Collisions
TypeCollision with vector velocities
DifficultyModerate -0.3 This is a straightforward application of conservation of momentum in two dimensions with coalescing particles. Students simply need to apply m₁u₁ + m₂u₂ = (m₁+m₂)v component-wise, requiring only routine algebraic manipulation with no problem-solving insight or multiple steps beyond the direct formula application.
Spec6.03c Momentum in 2D: vector form6.03d Conservation in 2D: vector momentum

1 Two particles, \(A\) of mass 7 kg and \(B\) of mass 3 kg , are moving on a smooth horizontal plane when they collide. Just before the collision, the velocity of \(A\) is \(( 3 \mathbf { i } + 8 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) and the velocity of \(B\) is \(( 6 \mathbf { i } - 5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). During the collision, the particles coalesce to form a single combined particle. Find the velocity of the single combined particle after the collision.

1 Two particles, $A$ of mass 7 kg and $B$ of mass 3 kg , are moving on a smooth horizontal plane when they collide. Just before the collision, the velocity of $A$ is $( 3 \mathbf { i } + 8 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ and the velocity of $B$ is $( 6 \mathbf { i } - 5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$. During the collision, the particles coalesce to form a single combined particle.

Find the velocity of the single combined particle after the collision.

\hfill \mbox{\textit{AQA M1 2012 Q1 [3]}}