# Bang bang, you shot me down...

A man sitting in a hot air balloon floating $$h$$ meters above the ground drops an object towards the ground, and at the same time fires a gunshot.

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
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