Challenging +1.2 This is a standard M4 oblique impact question requiring resolution of velocity components perpendicular and parallel to the plane, application of Newton's experimental law (e = speed of separation/speed of approach), and impulse calculation using momentum change. While it involves multiple steps and careful angle work, it follows a well-established method taught in M4 with no novel insight required. The 11 marks reflect the algebraic manipulation rather than conceptual difficulty.
A small smooth ball of mass \(m\) is falling vertically when it strikes a fixed smooth plane which is inclined to the horizontal at an angle \(\alpha\), where \(0° < \alpha < 45°\). Immediately before striking the plane the ball has speed \(u\). Immediately after striking the plane the ball moves in a direction which makes an angle of \(45°\) with the plane. The coefficient of restitution between the ball and the plane is \(e\). Find, in terms of \(m\), \(u\) and \(e\), the magnitude of the impulse of the plane on the ball.
(11)
A small smooth ball of mass $m$ is falling vertically when it strikes a fixed smooth plane which is inclined to the horizontal at an angle $\alpha$, where $0° < \alpha < 45°$. Immediately before striking the plane the ball has speed $u$. Immediately after striking the plane the ball moves in a direction which makes an angle of $45°$ with the plane. The coefficient of restitution between the ball and the plane is $e$. Find, in terms of $m$, $u$ and $e$, the magnitude of the impulse of the plane on the ball.
(11)
\hfill \mbox{\textit{Edexcel M4 2014 Q1}}