(a)
The factor
(a)
Answer to Problem 2SP
The factor
Explanation of Solution
Given info: The velocity of the pions with respect to the laboratory is
Write the expression to find the
Here,
Substitute
Conclusion:
Therefore, the factor
(b)
The half-life of the moving pions as seen by an observer in laboratory.
(b)
Answer to Problem 2SP
The half-life of the moving pions as seen by an observer in laboratory is
Explanation of Solution
Given info: The decay of pions at rest has a half-life of
Write the expression to find the half-life of the moving pions as seen by the observer in laboratory.
Here,
Substitute
Conclusion:
Therefore, the half-life of the moving pions as seen by an observer in laboratory is
(c)
The distance travelled by the pions before its half decay as measured in the laboratory.
(c)
Answer to Problem 2SP
The distance travelled by the pions before its half decay as measured in the laboratory is
Explanation of Solution
Given info: The velocity of the pions with respect to the laboratory is
Write the expression to find the distance travelled by the pion before it has decayed.
Here,
Substitute
Conclusion:
Therefore, the distance travelled by the pions before its half decay is
(d)
The distance travelled by the pions before the half decay from the reference frame of the pion.
(d)
Answer to Problem 2SP
The distance travelled from the reference frame of the pion is
Explanation of Solution
Write the expression to find the distance travelled from the reference frame of the pion.
Here,
Substitute
Conclusion:
Therefore, the distance travelled before the half decay from the reference frame of the pion is
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