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Problem 15 Easy Difficulty

A supertrain with a proper length of 100 $\mathrm{m}$ travels at a speed of 0.950 $\mathrm{c}$ as it passes through a tunnel having at proper length of 50.0 $\mathrm{m}$ . As seen by a trackside observer, is the train ever completely within the tunnel? If so, by how much do the train's ends clear the ends of the tunnel?

Answer

19 $\mathrm{m}$ to spare

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Video Transcript

well, the Observer majors the proper land off the Tomoo 50 meter proper leant off the tunnel. Lend off. The tunnel is equal to 50 meter. Uh, remember, this is Ah, the measurement of the observer. It's a proper land, but the observer measured the train contracted to limp. L is equal to L P. Times Square. Root off one minus. We squared, divided by C square. Uh, here, LP's 100 meter into square. Root off one minus. Is it a 10.95 all square, and therefore L is equal to 31.2 meter. Well, uh, this is shorter than the tunnel by 50 minus 31 point do, which is equal to 18.8 meter, which is around 19 meters. So, uh, this length is short than the tunnel by 19 meter. Ah, the creekside observer measures the length to be 31.2 meter. So the super eso the super train is majored to fit in the tunnel with ah, uh, around 19 meter, uh, to spare

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