A bird is sitting on the top of a vertical pole 20 m high and its elevation from the point O on the ground is 45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is

Engineering

Mathematics

problems on height and distance

Question

$40 (\sqrt{2} - 1)$

$20 (\sqrt{3} - 1)$

$20 \sqrt{2}$

$40 (\sqrt{3} - \sqrt{2})$

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In $∆$ AOB

$tan 45 º = \frac{20}{x} \Rightarrow x = 20$

In ΔDOC

$tan 3 0 º = \frac{20}{x + y}$

$\frac{1}{\sqrt{3}} = \frac{20}{20 + V}$

where V is speed in m/s

$V = 20 (\sqrt{3} - 1) m / s$