(5%) Problem 13: A free neutron lives 882 s when at rest relative to an observer

Question

(5%) Problem 13: A free neutron lives 882 s when at rest relative to an observer Randomized Variables to = 882 s t = 2100 s O A How fast is the neutron moving relative to an observer who measures its life span to be 2100 s? Give your answer in terms of c Grade Summary Deductions Potential 0% 100% Submissions Attempts remaining: 7 cos0 tan() | acos0 sin cotanas % per attempt) detailed view atanacotan) sinhO cosh0 tanh) cotanhO o Degrees o Radians 0 END BACKSPACE DELCLEAR Submit Hint I give up! Hints: 1 % deduction per hint. Hints remaining: 3 Feedback: 1% deduction per feedback.

Explanation / Answer

Ans:-

Using t = t0 , where ,= (1-(v^2/c^2))^-1/2

we see that =t /t0 =2100/882 = 2.3809

Squaring the equation gives ^2 = (c^2-v^2/C^2)^-1 = c^2/(c^2-v^2)

Cross-multiplying gives c^2- v^2 = c^2/^2

and solving for speed finally gives

v= sqrt (c^2 – c^2/^2)

= c sqrt (1 -1/ )

=c sqrt (1-1/(2.3809)^2)= 0.9075c

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