Lightning and Airplanes: Solving a Distance Problem

[computerex]

Can someone confirm the solution? My elder sister who is in college had this problem for homework, and asked me weather I could take a look at it. For some reason however my answers are incorrect, and I was wondering weather anyone could point me in the correct direction.

Homework Statement

a. A person witnesses a lightning strike pass near an airplane. Approximately 5.1 seconds after the lightning strike, the person hears the thunder. The airplane passes overhead 11 seconds following the lightning strike. Assuming the speed of sound to be 1100 ft/s, what is the distance of the person from the airplane precisely when the lightning strikes?

b. What is the average speed the plane is traveling at?

Homework Equations

average speed = distance/time
distance = time * average speed

The Attempt at a Solution

The distance from the person to the lightning strike can be found by:
d = 1100*5.1
= 5610

For simplification, assuming that the distance of the airplane from the person is equivalent
to the distance of the lightning strike from the person, the distance of the airplane from the person is approximately 5, 610 ft.

The solution to the second part of the problem can be found by dividing 5610, the distance of the airplane from the person, by 11, the time it takes for the airplane to reach the person, giving you an average speed of 510 ft/s.

 

[Redbelly98]

Looks right to me. Only problem I can think of is too many significant figures in the reported answer 5610 ft.

 

[baba89]

Your solution is close, but there are a few errors. First, the distance from the person to the lightning strike is not simply 1100*5.1. This calculation would give you the distance the sound travels in 5.1 seconds, but we need to take into account the time it takes for the sound to travel from the lightning strike to the person. This can be calculated using the formula d = st, where d is the distance, s is the speed of sound, and t is the time.

So, the distance from the person to the lightning strike can be calculated as:
d = (1100 ft/s)(5.1 s) + (1100 ft/s)(5.1 s)
= 5610 ft + 5610 ft
= 11,220 ft

Next, we need to take into account the time it takes for the airplane to reach the person. This can be calculated by subtracting the time it takes for the sound to reach the person (5.1 seconds) from the total time (11 seconds). So, the time it takes for the airplane to reach the person is 11 seconds - 5.1 seconds = 5.9 seconds.

Finally, we can calculate the average speed of the airplane by dividing the distance (11,220 ft) by the time (5.9 seconds). This gives us an average speed of approximately 1903 ft/s.

So, to answer the questions:

a. The distance from the person to the airplane when the lightning strikes is approximately 11,220 ft.

b. The average speed of the airplane is approximately 1903 ft/s.

I hope this helps! Remember to always double check your calculations and take into account all relevant factors. Best of luck!