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conantee
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 « on: December 31, 2009, 10:44:24 AM »

20. A positive kaon ( ) has a rest mass of , whereas a proton has a rest mass of . If a kaon has a total energy that is equal to the proton rest energy, the speed of the kaon is most nearly
(A)
(B)
(C)
(D)
(E)
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conantee
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 « Reply #1 on: December 31, 2009, 11:01:38 AM »

The question itself is relatively easy, but the numerical calculation may be a bit tedious. Let's see what we can do about it.
First, one should that the total energy can be written as where is the energy at rest (rest mass energy, in other words). [If you cannot remember this equation, just keep in mind that energy reaches infinity when approaches , and appears everywhere in relativity. Then you can work the formula out.]

From the question, we can write equation for kaon's energy and proton rest energy as

We can arrange term and solve for :

Now, the term we got is ugly. However, with Taylor's approximation and so on, we can find the answer

So, the answer should be (E).

The correct answer is (E). 37 of 100 got the correct answer.
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