An observer having a gun observes a remotely controlled balloon. When he first notices the ballo....

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An observer having a gun observes a remotely controlled balloon. When he first notices the balloon, it was at an altitude of \( 800 \mathrm{~m} \) and moving vertically upward at a constant velocity of \( 5 \mathrm{~m} / \mathrm{s} \). The horizontal displacement of balloon from the observer is \( 1600 \mathrm{~m} \). Shells fired from the gun have an initial velocity of \( 400 \mathrm{~m} / \mathrm{s} \) at a fixed angle \( \theta \).
( \( \sin \theta=3 / 5 \) and \( \cos \theta=4 / 5 \) ). The observer having gun waits (for some time after observing balloon) and fires so as to destroy the balloon. Assume \( g=10 \mathrm{~m} / \mathrm{s}^{2} \). Neglect air resistance.
After noticing the balloon, the time for which observer having gun waits before firing the shell is
\( \mathrm{P} \)
(1) \( 45 \mathrm{sec} \)
(2) \( 50 \mathrm{sec} \)
(3) \( 55 \mathrm{sec} \)
(4) \( 60 \mathrm{sec} \)


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