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Suppose a particle called a kaon is created by cosmic radiation striking the atmosphere. It moves by you at 0.980$c$ and it lives $1.24 \times 10^{-8}$ s when at rest relative to an observer. How long does it live as you observe it?

$\Delta t=6.23 \times 10^{-8} \mathrm{s}$

Physics 103

Chapter 28

Special Relativity

Relativity

Cornell University

Hope College

University of Sheffield

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the lost two of the Khan related to an observer addressed is ah, zero point mine it zero times the speed of light and the life of the calm. When a crest relative plane observer uh, the proper time Delton t not is equal to 1.24 Multiply by 10 to the power minus eight seconds. They're like mystic factor is given by one divided by square root off one minus We divided by sea whole square on, uh, Delta T, which is on dilated time Delta T is equal to proper time divided by a squared route off one minus we divided by sea whole square. Now let's find out the value of ah ah, real activist Ick factor Gamma is equal to one divided by square root off one minus. Uh, we we Is it a 0.980 times the speed of light divided by sea, whole square. And this gives us, um, this is equal to one divided by speared Rudolf one divided by square root off one minus 0.811 minus 0.81 And dan for their ladder. Mystic factor is equal to real idealistic factories equal to 5.255 point 05 And we know the Delta T is equal to gamma times that the tea not and then four. Uh, since comer is 5.0 to 5 and Delta T noughties 1.24 Multiply by 10 to the power minus eight on dhe solving, multiplying the two numbers. Delta T is equal to 6.2 tree multiply by 10 to the power minus eight seconds.

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