Calculating Speed and Time Between Two Vehicles Heading to Mars

[jono90one]

Homework Statement

You are in a vehicle heading towards Mars at constant speed. A superspeeder is going at constant speed 0.9c relative to you. When the superspeeder pases you, both times start at 0.

"At the point when you measure the superspeeder has traveled 1.4 x 10^7 m past you, what does the superspeeder read on their timer"

"At the point when the superspeeder reads the values calculated in previous question, what do you read on yours?"

Homework Equations

t=t0 gamma
s=d/t

The Attempt at a Solution

The first one i get 0.5 by just using speed = distance / time and re-aranging

But, I am sure which is t and t0, t0 is the proper time, but t0 is always smaller than t, so the thing going faster must always be t0 right?

So is t0 here the time the superspeeder reads?
(As i was told it was the other way around which has confused me :S)


Also for clarity, is t0 and l0 measured in the same frame of reference?

Thanks.

 

[Doc Al]

The first one i get 0.5 by just using speed = distance / time and re-aranging

That will tell you the time according to you, not according to the superspeeder. (But redo your calculation.)

But, I am sure which is t and t0, t0 is the proper time, but t0 is always smaller than t, so the thing going faster must always be t0 right?

Assuming you're talking about the time dilation formula, t0 is the proper time and is always the smaller number.

So is t0 here the time the superspeeder reads?

Yes.

Also for clarity, is t0 and l0 measured in the same frame of reference?

What is l0 ?

 

[jono90one]

lo is the proper length - not to do with this question but wanted to clarify l0 is in the same frame of reference has t0.

Well from what i understand there, i have started one correctly, but need to extend it using t = t0/(sqrt(1-(v/c)^2))

To find t0


Then for 2) it would simply be t? (which is t=d/v from 1), seems a little silly to word the questions this way if so)

also for t = d/v i got 0.05 (2dp) my bad.

Or have i miss understood?

 

[Doc Al]

lo is the proper length - not to do with this question but wanted to clarify l0 is in the same frame of reference has t0.

Yes. Example: A rocketship moving along. The proper length of the ship is its length as measured in its own frame. Similarly, the proper time is the time as measured by a clock in its own frame.

Well from what i understand there, i have started one correctly, but need to extend it using t = t0/(sqrt(1-(v/c)^2))

To find t0

Good.

Then for 2) it would simply be t? (which is t=d/v from 1), seems a little silly to word the questions this way if so)

Yes. (The parts would make more sense if given in the reverse order.)

also for t = d/v i got 0.05 (2dp) my bad.

Good.