The sound of a cannon firing is heard one sec | vedclass

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Question

(A) Let the position of the cannon be $P$ and the speed of sound be $S$.Let the time at which the sound of the cannon firing is heard at $A$ be $t$.Th

Vedclass · Accepted Answer

the positions $A$ and $B$ are foci of a hyperbola,with the cannon's position on one branch of the hyperbola

Vedclass · Answer

(A) Let the position of the cannon be $P$ and the speed of sound be $S$.Let the time at which the sound of the cannon firing is heard at $A$ be $t$.Therefore,the time at which it is heard at $B$ is $t+1$.Hence,the distance $PA = 	ext{Speed} 	imes 	ext{Time} = St$.Similarly,the distance $PB = S(t+1) = St + S$.Subtracting the two distances,we get $PB - PA = (St + S) - St = S$.Since $S$ is the speed of sound (a constant),$PB - PA = 	ext{constant}$.By the definition of a hyperbola,the locus of a point such that the difference of its distances from two fixed points (foci) is constant is a hyperbola.Thus,$A$ and $B$ are the foci of a hyperbola,and the cannon's position $P$ lies on one branch of this hyperbola.

The sound of a cannon firing is heard one second later at position $B$ than at position $A$. If the speed of sound is uniform,then

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