What lengths would be measured for two cars passing each other at 0.18c?

[catalyst55]

Hi,

This is the q. I'm pretty sure that they've got it wrong.

Two cars A and B pass each other at a speed of 0.18c. A person in car B says her car is 6.00m long and car A is 6.15m long. What does a person in car A measure for these two lengths?

Obviously, the person in car A would measure her car to be >6.15m long and car B to be <6.00m.

Because they pass each each at relativistic speeds, it would be prudent to use loretz transformations to find their relative speeds (even though galilean transformations would probably suffice).

speed relative to one another = (.18+.18)/(1+(.18*.18/1)) = (.18+.18)/1.0324 = .3487c (will use exact value though)

Thus, the length of car B is 6*1/loretz factor = 5.62m
and the lengh of car A is 6.15*loretz factor = 6.56m

the answers they get are 6.25m for car A and 5.90m for car B.

Am i right?

Thanks.

 

[nrqed]

Hi,

This is the q. I'm pretty sure that they've got it wrong.

Two cars A and B pass each other at a speed of 0.18c. A person in car B says her car is 6.00m long and car A is 6.15m long. What does a person in car A measure for these two lengths?

They pass each other at 0.18c...what does that mean? My interpretation is that each measures the speed of the other to be 0.18c. You seemed to assume that theyboth have a speed of 0.18c relative to a third observer but that does not seem to fit the question. With that speed, one gets their answer.

Patrick

 

[catalyst55]

They pass each other at 0.18c...what does that mean? My interpretation is that each measures the speed of the other to be 0.18c. You seemed to assume that theyboth have a speed of 0.18c relative to a third observer but that does not seem to fit the question. With that speed, one gets their answer.

Patrick

Ah, i see.

Thanks.