The angle of elevation of a jet plane from a point A on the ground is 60° . After a flight of 30 seconds, the angle of…

CBSE Class 10 Maths PYQ · Applications of Trig · Speed Distance · 5 Marks · March 2024 · Standard

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685 Marks · March 2024 · Standard
The angle of elevation of a jet plane from a point A on the ground is $60^\circ$. After a flight of $30$ seconds, the angle of elevation changes to $30^\circ$. If the jet plane is flying at a constant height of $3600 \sqrt{3} \text{ m}$, find the speed of the jet plane.
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Correct fig.
In $\triangle APB$
$\tan 60^\circ = \sqrt{3} = \frac{3600\sqrt{3}}{x}$
$x = 3600 \text{ m}$
In $\triangle AQC$
$\tan 30^\circ = \frac{1}{\sqrt{3}} = \frac{3600\sqrt{3}}{x+y}$
$x+y = 3600\sqrt{3} \times \sqrt{3} = 3600 \times 3 = 10800 \text{ m}$
$y = 10800 - x = 10800 - 3600 = 7200 \text{ m}$
speed of jet plane = $\frac{7200}{30} = 240 \text{m/sec}$
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