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This is problem (f) from the 2022 British Physics Olympiad Round 1. Fantastic problem, credit to the British Physics Olympiad. Please check out their excellent website and the problem here:
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Also please note that I am not affiliated with the British Physics Olympiad and my solution may be wrong (let me know in a comment if you think so). And as always with Olympiad Problems - there may be a much more efficient way of getting the problem or different ways of reaching it.

This is a Physics Olympiad Problem on motion, friction and can be used as an extension and challenge to A Level Physics Problems. It can also be used as preparation for the PAT and ESAT, entrance exams. As an extension it can be used to supplement problem solving in A Level Physics and similar courses such as AP Physics, IB Physics, CIE and others.

Chapters:
00:00 Understand the Problem
00:38 Use Energy Conservation if possible
01:02 Introduce variables, add them to diagrams
02:09 Use the Geometry for extra equations
03:26 Break down the problem into logical parts
05:36 Eliminate variables
06:51 Sometimes Slow is fast
07:39 Use Equations for Forces
08:58 Sanity Check on Answer

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