Search any question & find its solution
Question:
Answered & Verified by Expert
An aircraft is flying at a height of ' $H$ ' above the ground and at a speed of ' $V$ '. The maximum angle subtended at a ground observation point by the aircraft after time $T$ is
Options:
Solution:
2730 Upvotes
Verified Answer
The correct answer is:
$\tan ^{-1}\left(\frac{V T}{H}\right)$
Let $x$ is the distance travelled by the aircraft with speed $\mathrm{V}$ after time $\mathrm{T}$.
We get $\tan \theta=\frac{\mathrm{x}}{\mathrm{H}}$
Thus speed of the aircraft $\mathrm{V}=\frac{\mathrm{x}}{\mathrm{T}}$
$$
\begin{aligned}
& \mathrm{x}=\mathrm{VT} \\
& \theta=\tan ^{-1}\left(\frac{\mathrm{VT}}{\mathrm{H}}\right)
\end{aligned}
$$
We get $\tan \theta=\frac{\mathrm{x}}{\mathrm{H}}$
Thus speed of the aircraft $\mathrm{V}=\frac{\mathrm{x}}{\mathrm{T}}$
$$
\begin{aligned}
& \mathrm{x}=\mathrm{VT} \\
& \theta=\tan ^{-1}\left(\frac{\mathrm{VT}}{\mathrm{H}}\right)
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.