(a)
The length measured in the rest frame of the particle, if the length of the field between goal lines in the earth frame is
(a)

Answer to Problem 15P
The length measured in the rest frame of the particle is
Explanation of Solution
Since the length of the field between the goal lines in the rest frame of earth is
Write the expression for the length of field between the goal lines as measured in the rest frame of particle.
Here,
Write the expression for the Lorentz factor.
Here,
Substitute
Conclusion:
Substitute
Therefore, the length measured in the rest frame of the particle is
(b)
The time the particle takes to go from one goal line to the other according to Earth observers.
(b)

Answer to Problem 15P
The time the particle takes to go from one goal line to the other according to Earth observers is
Explanation of Solution
The speed of the particle is constant with respect to earth. Thus, the time can be found using the equation
Write the expression for the time taken by the particle to move from one goal line to another relative to earth observer.
Substitute
Conclusion:
Substitute
Therefore, the time the particle takes to go from one goal line to the other with respect to Earth observers is
(c)
The time the particle takes to go from one goal line to the other in the rest frame of the particle.
(c)

Answer to Problem 15P
The time the particle takes to go from one goal line to the other in the rest frame of the particle is
Explanation of Solution
In rest frame of the particle, the distance travelled is
Write the expression for the time required to travel between goal lines in the rest frame of the particle.
Here,
Conclusion:
Substitute
Substitute
Therefore, the time the particle takes to go from one goal line to the other with respect to rest frame of the particle is
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Chapter 26 Solutions
PHYSICS
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