# Bang bang, you shot me down...

**Classical Mechanics**Level 5

An observer on the ground, standing on the ground right next to the place of the impact of the object, measures a time difference \(\Delta t = 3s\) between the arrival of the sound of the shot and the impact of the object.

What is the sum of the two possible heights \(h_{1}\) and \(h_{2}\), if both heights are rounded down to the nearest lower integer?

\(\textbf{Details and assumptions}\)

- The temperature of the air is \(T = 14.5°C\)
- The ideal gas constant is \(R = 8.31 \frac {J}{mol \cdot K}\)
- The molecular mass of air is \(MM = 28.96 \frac {g}{mol}\)
- The adiabatic index of air is \(1.4\)
- The gravitational acceleration is \(g = 9.8 \frac {m}{s^2}\)
- For simplicity, round off the speed of sound \(v_{s}\) to the nearest integer
- Both heights \(h_{1}\) and \(h_{2}\) are rounded down to the nearest lower integer
*before*being added together - Assume no air drag acts upon the object