An aircraft is flying at a height of H above | vedclass

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Question

(A) Let the aircraft be at point $A$ at $t=0$ directly above the observer $O$ at a height $H$. After time $T$, the aircraft reaches point $B$ such tha

Vedclass · Accepted Answer

$	an ^{-1}\left(\frac{V T}{H}ight)$

Vedclass · Answer

(A) Let the aircraft be at point $A$ at $t=0$ directly above the observer $O$ at a height $H$. After time $T$, the aircraft reaches point $B$ such that the horizontal distance $AB = VT$.Let $\alpha$ be the angle subtended by the path $AB$ at the observation point $O$.The angle of elevation at $t=0$ is $	heta_1 = 0$ (if we consider the point directly overhead) or we look at the angle subtended by the segment $AB$.The angle $	heta$ subtended by the segment $AB$ at $O$ is given by $	heta = 	heta_2 - 	heta_1$, where $	heta_2 = 	an^{-1}(\frac{VT}{H})$ and $	heta_1 = 0$.Thus, the angle is $	an^{-1}(\frac{VT}{H})$.

An aircraft is flying at a height of $H$ above the ground at a constant speed $V$. What is the maximum angle subtended at a ground observation point by the aircraft's path after time $T$?

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