Challenging +1.2 This is a standard M4 differential equations problem requiring integration of the equation of motion with linear air resistance. While it involves multiple steps (setting up F=ma, separating variables, integrating, and finding when v=0), the technique is a core textbook method for this module with no novel insight required. The 8 marks reflect routine algebraic manipulation rather than conceptual difficulty.
A small ball of mass \(m\) is projected vertically upwards from a point \(O\) with speed \(U\). The ball is subject to air resistance of magnitude \(mkv\), where \(v\) is the speed of the ball and \(k\) is a positive constant.
Find, in terms of \(U\), \(g\) and \(k\), the maximum height above \(O\) reached by the ball.
(8)
A small ball of mass $m$ is projected vertically upwards from a point $O$ with speed $U$. The ball is subject to air resistance of magnitude $mkv$, where $v$ is the speed of the ball and $k$ is a positive constant.
Find, in terms of $U$, $g$ and $k$, the maximum height above $O$ reached by the ball.
(8)
\hfill \mbox{\textit{Edexcel M4 2014 Q3}}