Challenging +1.2 This is a standard M3 oblique collision problem requiring conservation of momentum along the line of centres, Newton's restitution law, and the given constraint that B moves at 45° after collision. While it involves multiple equations and careful component resolution, it follows a well-established method taught in M3 with no novel insight required—moderately above average difficulty due to the algebraic manipulation needed.
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\includegraphics[max width=\textwidth, alt={}, center]{08760a55-da6c-41f2-a88a-289ecc227f69-2_421_759_936_694}
Two uniform smooth spheres \(A\) and \(B\), of equal radius, have masses 2 kg and 3 kg respectively. They are moving on a horizontal surface when they collide. Immediately before the collision, \(A\) has speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is moving along the line of centres, and \(B\) has speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is moving perpendicular to the line of centres (see diagram). The coefficient of restitution is 0.6 . The direction of motion of \(B\) after the collision makes an angle of \(45 ^ { \circ }\) with the line of centres. Find the value of \(v\).
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\includegraphics[max width=\textwidth, alt={}, center]{08760a55-da6c-41f2-a88a-289ecc227f69-2_421_759_936_694}
Two uniform smooth spheres $A$ and $B$, of equal radius, have masses 2 kg and 3 kg respectively. They are moving on a horizontal surface when they collide. Immediately before the collision, $A$ has speed $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and is moving along the line of centres, and $B$ has speed $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and is moving perpendicular to the line of centres (see diagram). The coefficient of restitution is 0.6 . The direction of motion of $B$ after the collision makes an angle of $45 ^ { \circ }$ with the line of centres. Find the value of $v$.
\hfill \mbox{\textit{OCR M3 2010 Q2 [7]}}