There are two particles $A$ and $B$ with particle $A$ at $\left( -13,\ 0 \right)$ and partic

Question

There are two particles $A$ and $B$ with particle $A$ at $\left( -13,\ 0 \right)$ and particle $B$ at $\left( 0,\ -9 \right)$ with respect to origin $O$. $A$ moves towards $O$ at a constant speed of $u\ \mathrm{cm}\,{{\mathrm{s}}^{-1}}$ in the positive $x$ direction and $B$ moves towards $O$ at a constant speed of $\frac{4}{3}u\ \mathrm{cm}\,{{\mathrm{s}}^{-1}}$ in the positive $y$-direction (see diagram). Show that, after a time of $t$ seconds, the distance between $A$ and $B$ is given by $\sqrt{\left( \frac{25}{9}{{u}^{2}}{{t}^{2}}-50ut+250 \right)}$ cm.[2] Find the coordinates of $A$ and $B$ at the instant when the two particles are closest.[4]

Accepted Answer

$AB=\sqrt{\frac{25}{9}u^2t^2-50ut+250}\text{ cm}$, with closest positions $A=(-4,0)$ and $B=(0,3)$

2013 HCI P1 Q3

2013 HCI P1 Q3

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