Superman is a character from the DC Comics universe with superhuman abilities. One day in the city of Metropolis you look to the skies only to see Superman passing directly over your head as he races to save Lois Lane from some imminent threat. Not in too much of a rush, Superman is cruising along a ta comfortable mach 4, 1 km above the ground. He yells out directions but because sound travels much slower than light, how far away is he when you hear him(ie. the actual distance from you on the ground to him in the air)? Speed of Sound = 340m/s.

Question

Superman is a character from the DC Comics universe with superhuman abilities. One day in the city of Metropolis you look to the skies only to see Superman passing directly over your head as he races to save Lois Lane from some imminent threat. Not in too much of a rush, Superman is cruising along a ta comfortable mach 4, 1 km above the ground. He yells out directions but because sound travels much slower than light, how far away is he when you hear him(ie. the actual distance from you on the ground to him in the air)? Speed of Sound = 340m/s.

Answer 1

c = speed of sound

4 c = speed of superman

t = time for signal to reach ground = 1000/c
t is also how long he flew beyond the yell
so he flew x = 4 c (1000/c) = 4000
hypotenuse = sqrt (1000^2 + 4000^2)
=sqrt (10^6 + 16* 10^6)
= 1000 sqrt 17 meters
or
sqrt 17 kilometers

note: since the super speed is given in mach, the actual speed is not needed.

Answer 2

Thanks you so much!

I just saw that there was a part two in which it says, "what does it sound like when you hear his sentence?" He said, "Hey! Finish your test!"
I don't know how to answer this...?

Answer 3

To determine the distance between you on the ground and Superman in the air when you hear him, you can use the formula:

Distance = Speed × Time

In this case, the speed we are interested in is the speed of sound, which is given as 340m/s.

To find the time it takes for the sound to reach you, we need to calculate the time it takes for Superman's voice to travel from him to you.

Since he is moving at a constant speed of mach 4, which is four times the speed of sound, his speed is 4 × 340 m/s = 1360 m/s.

Now, we can calculate the time it takes for the sound to reach you by dividing the distance Superman has traveled (1 km or 1000 meters) by his speed (1360 m/s):

Time = Distance / Speed = 1000 m / 1360 m/s ≈ 0.735 seconds

Therefore, it takes approximately 0.735 seconds for the sound to reach you.

Now, to find the distance between you and Superman when you hear him, we multiply the speed of sound by the time it takes for the sound to reach you:

Distance = Speed of Sound × Time = 340 m/s × 0.735 s ≈ 249.9 meters

Therefore, when you hear Superman's voice, he is approximately 249.9 meters away from you in the air.