- #1
Abu
- 39
- 16
Homework Statement
A man is flying with a speed of 0.7c and at a height 1 km. During his flight, he measures the distance between Toronto and Montreal to be 450 km. What is the real distance between them.
I don't think the answers are based on real life, they are just examples of places.
Homework Equations
t = to / √1-(v/c)2
The Attempt at a Solution
So if they are flying at 0.7c, that means they are flying at
0.7 x 3x10^8 = 2.1 x 10^8 m/s
Which means that they would cover 450 km, or 450000 meters, in 0.002142 seconds (I don't think the height of 1 km matters in this question, but correct me if I am wrong)
What I'm struggling with is the formula. I'm not sure where to put the numbers. From what I know, as you go faster, time increases slower. Since the man measured 0.002142 seconds, this is the dilated time, right? Meaning that this value of 0.002142 should be larger for an observer on earth. So for that reason, I want to put this value of 0.002142 as the t variable, instead of the to variable.
I think what is confusing me is which version of t is the dilated time. I've seen other versions of this time dilation formula without the division sign between to and the 1-(v/c)2
Thank you for your patience and time. If anything I said was not clear, please don't hesitate to ask me and I'll clarify my question.
Thank you!