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Problem 18 Easy Difficulty

A spacecraft with a proper length of $L_{p}$ passes by an observer on the Earth. According to this observer, it takes a time interval $\Delta t$ for the spacecraft to pass a fixed point. Determine the speed of the object as measured by the Earth-based observer.

Answer

$\frac{\left(L_{p} / \Delta t\right)}{\sqrt{\left(1+\left(\frac{L_{p}}{\Delta t c}\right)^{2}\right.})}$

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Video Transcript

well, the spaceship is measured by articles. There were to be your friend. L and L is equal to L P Times Square root off one minus re squared, divided by C squared and also at least equal to three times done to t right. And before we every time still to t is equal to help you Times square root off one minus We squared, divided by C square All right, Taking sweat on both sides We have re square Don't A T square is equal to hell. Peace Fear into one minus. These were divided by C Square. No, let's sold for me. No solving for we we have here already is equal to ah see times l p divided by, um screen Rudolph C Square Dr D Square less I'll be square.

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