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.

Damon · Answer

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.

Ellie · Answer

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...?