At the instant $t = 0$, vehicle A is travelling due east at a constant speed of $20$ m/s from th

Question

At the instant $t = 0$, vehicle A is travelling due east at a constant speed of $20$ m/s from the origin $O$ and vehicle B is travelling due south at a constant speed of $10$ m/s from point $P$ that is $100$ m from $O$. The position of the two vehicles at $t = 0$ is shown in the diagram. Show that, at any time $t$, the distance between the two vehicles $D$ m, is given by $D = 10\sqrt{5(t^2 - 4t + 20)}.$ Find the instant when $D$ has a stationary value. Hence determine the nature of this stationary value and find its value.

Accepted Answer

(i) $D=10\sqrt{5(t^2-4t+20)}$ (ii) $t=2\text{ s}$ (iii) Minimum distance $=40\sqrt5\text{ m}$

Differentiation - Problems Involving Maximisation and Minimisation

Differentiation - Problems Involving Maximisation and Minimisation

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