Challenging +1.2 This is a standard M4 differential equations problem requiring separation of variables and integration with air resistance. While it involves multiple steps (setting up F=ma with resistance, separating variables, integrating, applying limits), the method is routine for M4 students and follows a well-practiced template. The 8 marks reflect length rather than conceptual difficulty, making it moderately above average but not requiring novel insight.
A ball of mass \(m\) is thrown vertically upwards from the ground with an initial speed \(u\). When the speed of the ball is \(v\), the magnitude of the air resistance is \(mkv\), where \(k\) is a positive constant.
By modelling the ball as a particle, find, in terms of \(u\), \(k\) and \(g\), the time taken for the ball to reach its greatest height. [8]
A ball of mass $m$ is thrown vertically upwards from the ground with an initial speed $u$. When the speed of the ball is $v$, the magnitude of the air resistance is $mkv$, where $k$ is a positive constant.
By modelling the ball as a particle, find, in terms of $u$, $k$ and $g$, the time taken for the ball to reach its greatest height. [8]
\hfill \mbox{\textit{Edexcel M4 2002 Q2 [8]}}