Question

height of firework
use the temperature of the air to find the speed of sound and use the time for the sound to arrive to find the total distance from person to explosion
finally, find the height of the firework when it exploded realizing that the picture below is not to scale
enter answers dont include units
speed of sound (m/s):
total distance (m):
height of explosion (m):

Explanation:

Step1: Find speed - sound formula

The speed of sound $v$ in air can be approximated by the formula $v = 331 + 0.6T$, where $T$ is the temperature of the air in degrees Celsius. Since the temperature is not given, if we assume standard - temperature conditions ($T = 20^{\circ}C$), then $v=331 + 0.6\times20=331 + 12 = 343$ m/s.

Step2: Calculate total distance

The time for the sound to arrive $t = 3947$ ms $=3.947$ s. Using the formula $d=v\times t$, with $v = 343$ m/s and $t = 3.947$ s, we get $d=343\times3.947=1353.821$ m.

Step3: Assume horizontal distance negligible

If we assume that the horizontal distance from the person to the point directly below the explosion is negligible (or that we are dealing with a situation where the line - of - sight is close to vertical), the height of the explosion $h$ is approximately equal to the total distance $d$. So $h = 1353.821$ m.

Answer:

Speed of Sound (m/s): 343
Total Distance (m): 1353.821
Height of Explosion (m): 1353.821