Exam-Style Problem
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May/June 2026 p42 q4
4338
A particle \(P\) is projected from a point \(A\) with speed \(4\text{ m s}^{-1}\) up a line of greatest slope of a rough plane inclined at an angle \(\theta\) to the horizontal, where \(\tan\theta=\frac43\).
\(P\) comes to instantaneous rest at a point \(B\) on the plane (see diagram).
The coefficient of friction between \(P\) and the plane is \(\frac13\).
(a) Using an energy method, show that the distance \(AB\) is \(0.8\text{ m}\).
(b) After coming to instantaneous rest at \(B\), the particle slides down the plane.
Find the total time from the instant at which \(P\) is projected from \(A\) until it returns to \(A\).
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