Question

In the festivities of my village, it is a tradition to blow up a fireworks display on the last day of the festivities. I'm always afraid to get too close, so I try to get as far away as possible. If my friend, who was just below where the rockets were exploding, heard the explosion 5 tenths of a second after seeing the lights, and I heard them 6 tenths of a second later:

a. How high do the rockets explode?
b. How far away were you from my friend?

Answer 1

The height at which the fireworks explode can be calculated by multiplying the speed of sound by the time delay (0.5 s) for the first observer, which results in approximately 173 meters. The additional distance between the two friends is determined by the extra time (0.1 s) it took for the sound to reach the second observer, which equates to roughly 34.6 meters.

Step-by-step explanation:

The question involves calculating the height of a fireworks explosion and the distance from one observer to another, based on the time lag between seeing and hearing the explosion. To do this, we use the fact that sound has a finite speed, which is influenced by air temperature. At 24°C, the speed of sound in air is approximately 346 meters per second. Given that one friend heard the explosion 5 tenths of a second after seeing it, and the other heard it 6 tenths of a second later:

• To find the height of the rockets, we use the first friend's experience. Since it took 0.5 seconds for the sound to reach them, we multiply this time by the speed of sound at 24°C to find the height, which is approximately 173 meters (0.5 s × 346 m/s).
• To calculate the additional distance between the second friend and the first, we can multiply the time difference (which is 0.1 second, the difference between 6 tenths and 5 tenths) by the speed of sound to get approximately 34.6 meters (0.1 s × 346 m/s).

Note that since the speed of light is much faster than the speed of sound, the delay caused by the light travel time is negligible and hence not considered here.