Question

Suppose a pole vaulter, holding a 16 unit long pole parallel to his direction of motion, runs through an 8 unit long shed which is open at each end. At what speed should a pole vaulter be running such that the pole is entirely in the shed before it strikes the exit door?

Answer 1

$let's\ assume\ that \;the\ length\ of \;the\ pole\\ resting \;relative\; to\\ the \;shed\; is\; equal \;to\ L=16\ unit\\ then\ according\ to\; the \;Lorentz\ transformations\\(by\ the\ terms) \;the\ length\ of\ a\ pole\\ moving\ relative \;to\ a\ shed\\ at\ the\ speed\ of\ v\ is\ equal\ to\;\frac{L}{2}=8\;unit .\;So\\\frac{L}{2}=L\sqrt{1-\frac{v^2}{c^2}}; \sqrt{1-\frac{v^2}{c^2}}=\frac{1}{2};\\1-\frac{v^2}{c^2}=\frac{1}{4}; v=\frac{c}{2}\sqrt{3}; v=\frac{3\times10^8}{2}\times1.73;\\v=2.6\times10^8\frac{m}{c}.\\Answer: v=2.6\times10^8\frac{m}{c}\;or\; v=0.87c$