Question

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. height of explosion (m): total distance (m): speed of sound (m/s): enter answers dont include units check 30°c 1335 m 3947 ms

Explanation:

Step1: Find speed of sound at 30°C

The speed of sound $v$ in air can be approximated by the formula $v = 331+ 0.6T$, where $T$ is the temperature in Celsius. Substituting $T = 30^{\circ}C$, we get $v=331 + 0.6\times30=331+18 = 349$ m/s.

Step2: Calculate total distance

We know that the time $t$ for the sound to reach the person is $t = 3947$ ms $=3.947$ s. Using the formula $d=v\times t$, with $v = 349$ m/s and $t = 3.947$ s, we have $d=349\times3.947\approx1377$ m.

Step3: Determine height of explosion

The height of the explosion is given as 1335 m.

Answer:

Height of Explosion: 1335
Total Distance: 1377
Speed of Sound: 349