A small ball $B$ of mass $0.2\,\text{kg}$ travels through a narrow fixed smooth cylindrical tube $OA$ of length $1\,\text{m}$, which is sealed at $A$. If the ball is at displacement $x\,\text{m}$ from $O$, its velocity is $v\,\text{m s}^{-1}$ in the direction $OA$ and a resisting force of magnitude $\frac{k}{1-x}\,\text{N}$ acts on it.
(i)[6]
The tube is fixed horizontally and $B$ is projected from $O$ towards $A$ with velocity $1.2\,\text{m s}^{-1}$. Given that $B$ comes to instantaneous rest after travelling $0.55\,\text{m}$, show that $k = 0.1803$, correct to $4$ significant figures.
(ii)[4]
The tube is now arranged vertically, with $O$ above $A$. The ball $B$ is let go from rest at $O$. Calculate the speed of $B$ once it has descended $0.1\,\text{m}$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies N2L, giving the single-force equation $0.2a = -\dfrac{k}{1-x}$” …