Answer:
1350 m/s
Clarification:
Bullet speed
The bullet travels 450 m
Sound travels a distance of 450 m
Using the equation S= V × t
==> t= S/V
Thus, the time for the bullet t1=450/vb
and the sound's travel time t2=450/vs
Given that there's a 1/2 sec interval from when the shot is fired to the moment the shooter hears the sound
==> t1+t2= 1/2 sec
==> 450/vb+450/vs=0.5sec ---- (1)
At a distance 'x' from both the gun and target, it takes 3 seconds for a person to hear the bullet sound from firing to impact.
Firing sound duration
n
Distance =x m
Speed of sound = V
time =T1
==> T1 = x/vs
During this time period, the bullet covers 450 m and the sound of impact travels a distance 'x'
The time taken for sound = 450/vb
The time it takes sound to travel distance 'x'= x/vs
therefore let T2= 450/vb + x/vs
However, all this occurs within 3 seconds, i.e., T = 3 sec
because firing takes place before hitting the target, implying the strike sound is heard in time T = T2-T1= 450/vb + x/vs -x/vs
Making T= 3sec
==> 3= 450/vb
==> vb= 1350 m/s
From equations 1 and 2
applying the same principle, in 3 seconds the observer sees the bullet travel 450 m and perceives the sound
