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Problem 13 Easy Difficulty

A super train of proper length $1.00 \times 10^{2} \mathrm{m}$ travels at a speed of 0.95$c$ as it passes through a tunnel having proper length 50.0 m. As seen by a track side observer, is the train ever completely within the tunnel? If so, by how much?

Answer

19m

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Video Transcript

using L physical to proper lend times squared Rudolph one minus well, we squared, divided by cease were well in this case, proper land is equal to 100 meters, 100 meters and therefore angle is equal to we're also even be. We is equal to zero point buying five times the speed of light. So Al is equal to 100. Multiply by squared Rudolph one minus hoese Tzeitel point 95 times c all square divided by C square and L is equal to 100. Um, multiply by one minus 0.95 whole square, zero point mine by all square and this gives us 90 meters.

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