Question

One normal afternoon in undisclosed City X, the chocolate factory workers overload the Easter egg machine. A group of angsty teens cutting school at the edge of City X see a large explosion from across town as the factory explodes, covering the rooftops in unrefined sugars. Five seconds later, they hear the boom. Approximately how far are they from the factory? show work

A. 68.6 m
B. 145 m
C. 1,715 m
D. 60,000 m

Answer 1

The correct option is;

C. 1,715 m

Step-by-step explanation:

We are given the information from the group of teen at the City edge

Time of arrival of explosion sound = 5 s after sighting

Time of sighting explosion = 5 s before hearing the boom

Speed of sound in air ≈ 343 m/s

Speed of light = 299,792 km/s

Therefore, distance covered by sound in 5 seconds is given by the following equation;

`Speed = (Distance)/(Time)`

`\therefore 343 \ m/s= (Distance)/(5 \, s)`

Hence Distance = 343 m/s × 5 s = 1715 m

To check, we compare the time it would take for the light to cover 1715 m

That is
`Time = (Distance)/(Speed) = (1715)/(299,792,000) = 0.00000572 \, s` which is instantaneous hence the distance can be approximated by the time duration for the speed of sound.

Therefore, the distance of the students from the factory is approximately 1,715 m