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The sound of a cannon firing is heard one second later at a position $B$ that at position $A$. If the speed of sound is uniform, then
the positions $A$ and $B$ are foci of a hyperbola, with cannon's position on one branch of the hyperbola
the position $A$ and $B$ are foci of an ellipse with cannon's position on the ellipse
one of the positions $A, B$ is focus of a parabola with cannon's position on the parabola
it is not possible to describe the positions of $A, B$ and the cannon with the given in formation
Solution
(a)
Let the position of cannon $=P$ speed of sound $=S$
Time of heard of sound of cannon firing of at $A=t$
$\therefore$ at $B=t+1$
Hence, $P A=$ Speed $\times$ Time
$P A=S t$
$and\,P B=S(t+1)=S t+S$
$P B-P A=S t+S-S t$
$P B-P A=S$
$P B-P A=$ constant
$\therefore A$ and $B$ are foci of hyperbola.
