How Do You Calculate Time Difference in Different Inertial Systems?

[jimmypoopins]

Homework Statement

Two events occur in an inertial system at the same time, but 9000 km apart. However in another inertial system these two events are observed to be 11000 km apart.

What is the time difference between the two events in this second inertial system?

Homework Equations

s^2=x^2+y^2+z^2-(ct)^2

The Attempt at a Solution

since the spacetime interval is invariant in any inertial frame, s^2 can equal s'^2
for the first inertial system i got s^2=9m^2
putting it into the second equation i got
9m^2=11m^2-(ct)^2
subtracting 11m^2, dividing by -c, and taking the square root, i am left with 2.108*10^-8sec, which seems like it could be a reasonable answer, but it is not correct.

can anyone tell me what i am doing wrong and lead me in the right direction please?

 

[nrqed]

Homework Statement

Two events occur in an inertial system at the same time, but 9000 km apart. However in another inertial system these two events are observed to be 11000 km apart.

What is the time difference between the two events in this second inertial system?

Homework Equations

s^2=x^2+y^2+z^2-(ct)^2

The Attempt at a Solution

since the spacetime interval is invariant in any inertial frame, s^2 can equal s'^2
for the first inertial system i got s^2=9m^2
putting it into the second equation i got
9m^2=11m^2-(ct)^2
subtracting 11m^2, dividing by -c, and taking the square root, i am left with 2.108*10^-8sec, which seems like it could be a reasonable answer, but it is not correct.

can anyone tell me what i am doing wrong and lead me in the right direction please?

You have the right idea, it just seems that you are making some algebra mistake. First, it is 9000 km apart so $9 \times 10^6 m$. Second, when solving for the time interval in the other frame, you must divide by the square of c before taking the square root.

 

[jimmypoopins]

ah you are right, thank you. for some reason when i saw 4000km i assumed that i had to divide by 1000 to get it in meters. i don't know why, a stupid mistake on my part.