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

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When two cars, A and B, pass each other at a speed of 0.18c, the lengths measured by observers in each car differ due to relativistic effects. A person in car A would measure car B's length to be shorter than 6.00m and car A's length to be longer than 6.15m, which is consistent with Lorentz transformations. The calculations show that car B's length would be approximately 5.62m and car A's length about 6.56m when accounting for relativistic effects. There is some confusion regarding the interpretation of their relative speeds, as both observers perceive each other moving at 0.18c. Ultimately, the discussion highlights the importance of correctly applying relativistic principles to measure lengths in high-speed scenarios.
catalyst55
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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.
 
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catalyst55 said:
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
 
nrqed said:
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.
 
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