The diagram below shows an isosceles triangle $ABC$ with fixed lengths $AB$ and $AC$ of $10$cm each.

Question

The diagram below shows an isosceles triangle $ABC$ with fixed lengths $AB$ and $AC$ of $10$cm each. $A$ is a variable point which is at a height $h$ cm directly above the point $O$ while $B$ and $C$ are variable points which move horizontally along the line $l$.

Given that $A$ descends vertically towards the point $O$ such that the area of triangle $ABC$ is decreasing at a constant rate of $0.7$ cm$^{2}$/s, determine at the instant when $A$ is $6$ cm above $O$,

the rate of change of $\theta $,
the rate at which $C$ is moving away from $O$.

Accepted Answer

$\frac{d\theta}{dt} = -\frac{1}{40}$ rad/s, $\frac{dx}{dt} = \frac{3}{20}$ cm/s

NJC Applications of Differentiation Tutorial Q9

NJC Applications of Differentiation Tutorial Q9

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