Relativity question involving time dilation

[schattenjaeger]

An observer on a spacecraft moving .6c relative to the Earth finds that a car takes 50 minutes to take a trip. How long does the trip take the driver of the car?(the problem just glosses over the 50mph or so the car would be going)

Ok, so v=.6c, and we're using the lorentz transformation for time, so
To=gamma*T and where I always get mixed up is which T is which value

if you think from the perspective of the car, we're told in the problem that 50 minutes elapses on the ship, so t=50, and we solve for To which is about 40.

It's too late for me think about if that's right, but...it is, isn't it? Since the car is moving .6c relative to the ship, it's ticking slow, if you will

but shouldn't you be able to do it the other way, from the perspective of the ship? So To=50 and solve for T which is like 62.5 and my head thusly explodes

 

[gnpatterson]

The point is that this is a relativity question. Think of it in terms of stationary ship that has a planet fly past at 0.6c. On the planet a journey (any process) appears to take 50 mins. You should have a feeling about what time dilation does and so you should realize what is happening in each frame of reference. If the car driver and the astronaut have a conversation after the event they should be able to agree on exactly what happened with each others clocks and the exact (apparent) timing of events in each frame of reference.

 

[Curious3141]

The proper time interval, which is the time interval measured when the observer/timepiece is at rest relative to the traveller, is always the shortest. The clock in the car is at rest relative to the car and its passengers, so this is the proper time interval. It should be less than 50 mins.

 

[schattenjaeger]

ohh, ok, thanks, I got it right on what I turned in. I think I've got the concept on the tip of my brain, I can do all the other problems involving time dilation and length contraction easily enough, but for some reason this one confuses me.

So, the time interval measured when the observer is at rest relative with the travellor is the proper time? So in this case the 50 minutes is NOT the proper time, that's the measured elapsed time from the moving frame, so it should 50=formula which results in 40, right?

 

[Curious3141]

ohh, ok, thanks, I got it right on what I turned in. I think I've got the concept on the tip of my brain, I can do all the other problems involving time dilation and length contraction easily enough, but for some reason this one confuses me.

So, the time interval measured when the observer is at rest relative with the travellor is the proper time? So in this case the 50 minutes is NOT the proper time, that's the measured elapsed time from the moving frame, so it should 50=formula which results in 40, right?

Correct.

 

[schattenjaeger]

Something's still fishy about this to me.

I missed perhaps an important word in the question statement, it asks how long the trip takes TO the driver of the car

So if the driver of the car is puttering along and he knows that 50 minutes elapsed on the spaceship, MORE time should elapse to him, since the ship's clock is ticking slow, right?