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Please Help Me With This Physics Exercise

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mufarrid | 21:55 Thu 13th Jan 2022 | Science
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How fast will a 4-meter long car need to go in order to fit inside of a 3-meter long garage? (answers in terms of c, the speed of light)

Thanks in advance!

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This may help?
https://science.howstuffworks.com/science-vs-myth/everyday-myths/relativity9.htm
Good luck I would'nt know where to start
so about two thirds?.... but does it really fit in or is it just it look's smaller???
I wouldn't really work, though, would it. To avoid the car colliding with the end wall of the garage, it too (the garage) would have to travel at the same speed as the car and so be subject to the same shortening.
I'm sure that if the rear wall were reinforced and the car were entering the garage at about 30-50 mph, it would end up actually 3m in length (if not shorter) rather than appearing to be 3m in length...
What's the colour of the car?
I think it would be the colour blur.
red shift maybe
I actually tried this once as I have a similar sized car and garage.

I only got one go at it because the car was a write off afterwards, but what I can say is that it needs to be faster than 65 mph.
Incredz Lorentz around 30 y before Einstein did his stuff
said, "if you reduce by 1 - v2/c2 - square root of.... ( look p Lorentz contraction) - call this r, then it all comes out in the wash"

can anyone see the speed is gonna have to be half-c ?

L = Lo times r - - - - -r here is 1 minus v2/c2 ( sq rt)
3 = 4 r leads to 9/16 = r2
kick around - - 7 /16 = v2/c2
so v is root7 / 4 times c

I can do it better on a piece of paper - google Lorentz contraction

Now seriously folks
this is a classical problem
Car is 1 cm longer than the garage
the car goes at such a speed that it is now the length of the garage by reason of Lorentz contraction - that pretty near 'c' !

as the car exhaust passes an observer at the door, he closes it.
What happens then ?

( does the back of the car explode thro the garage doors a fraction of a second later?)

and and and the answer is....

time is local so the observer's time is t1 and the drivers time is t2
and they are not able to agree when the car has completely passed into the garage

Physics course 1970

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