Relative speed and Time dilation

[stellaman]

Homework Statement

What is the relative speed if two observers record a time difference of 1%

Homework Equations

t=(gamma)t'

The Attempt at a Solution

I use the above equation and solved for v, and got

v=sqrt(-c²((t'/t)²-1)

however I am gettin 2.999x10⁸m/s, and I am pretty sure that is not right.

 

[DukeLuke]

Perhaps you can relate $\frac{t}{t'}$ to the 1% time difference. If you can do this you could find a velocity by solving $\frac{t}{t'} = \gamma$ for the v in gamma.

 

[nlightner]

I would suggest checking your calculations and making sure you are using the correct units. The value you have calculated for the relative speed seems to be too high, as it is approaching the speed of light. It is important to remember that time dilation occurs when an object is moving at a significant fraction of the speed of light, so the relative speed between the two observers should also be a fraction of the speed of light. Additionally, it would be helpful to know the specific scenario in which the time difference of 1% was recorded, as this could provide more context for the relative speed calculation. I would recommend double-checking your calculations and units, and possibly seeking clarification on the given information to ensure an accurate answer.