Challenging +1.2 This is a standard M3 oblique collision problem requiring resolution of velocities parallel and perpendicular to the line of centres, application of conservation of momentum and Newton's restitution law, then recombination. It's methodical but involves multiple steps and careful component work, making it moderately harder than average A-level questions but still a textbook exercise type.
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\includegraphics[max width=\textwidth, alt={}, center]{85402f4a-8d55-47d8-ba48-5b837609b0f4-2_387_561_1055_794}
Two uniform smooth spheres \(A\) and \(B\), of equal radius, have masses 0.8 kg and 2.0 kg respectively. The spheres are on a horizontal surface. \(A\) is moving with speed \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at \(60 ^ { \circ }\) to the line of centres when it collides with \(B\), which is stationary (see diagram). The coefficient of restitution between the spheres is 0.75 . Find the speed and direction of motion of \(A\) immediately after the collision.
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\includegraphics[max width=\textwidth, alt={}, center]{85402f4a-8d55-47d8-ba48-5b837609b0f4-2_387_561_1055_794}
Two uniform smooth spheres $A$ and $B$, of equal radius, have masses 0.8 kg and 2.0 kg respectively. The spheres are on a horizontal surface. $A$ is moving with speed $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at $60 ^ { \circ }$ to the line of centres when it collides with $B$, which is stationary (see diagram). The coefficient of restitution between the spheres is 0.75 . Find the speed and direction of motion of $A$ immediately after the collision.
\hfill \mbox{\textit{OCR M3 2008 Q3 [10]}}