How to tell how far bullet went using sound

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To determine the distance to the target after firing a rifle, the bullet's muzzle speed is 170 m/s, and the sound of the bullet striking the target is heard 1.30 seconds later. The speed of sound at 72°F is calculated to be approximately 344.32 m/s. The equation used combines the distances traveled by both the bullet and the sound, ensuring they cover the same distance in the given time. The relationship established is that the bullet travels for time 'x' while the sound travels for the remaining time (1.3 - x). This approach allows for calculating the distance to the target accurately.
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Homework Statement



A person holds a rifle horizontally and fires at a target. The bullet has a muzzle speed of 170 m/s, and the person hears the bullet strike the target 1.30 s after firing it. The air temperature is 72°F. What is the distance to the target?

Homework Equations


Vc=331+(0.6*T)
Vc= speed of sound through dry air (m/s)
T= temperature(Degrees C)



The Attempt at a Solution


Vc=331+(0.6*22.2)=344.32m/s
170x+344.32(1.3-x)=D
 
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One more condition: the bullet has to travel exactly as far in getting to the target as the sound does in traveling back.
 
Thank you. Got it
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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