Two rockets, A and B, approach each other as shown in the figure. A travels to the right at 0.7c while B travels to the left at 0.8c. Both speed measurements are made relative to an inertial observer.
-Both rockets have a supply of unstable mesons with a mean proper lifetime of 2.6 × 10^-⁸ s. Which one of the following is a correct observation for the inertial observer?

Question

Two rockets, A and B, approach each other as shown in the figure. A travels to the right at 0.7c while B travels to the left at 0.8c. Both speed measurements are made relative to an inertial observer.

-Both rockets have a supply of unstable mesons with a mean proper lifetime of 2.6 × 10^-⁸ s. Which one of the following is a correct observation for the inertial observer?

Quizplus · Accepted Answer

From the perspective of the inertial observer, both rockets are moving relative to them at different velocities. This means that in each rocket, time appears to be passing differently due to time dilation. Therefore, the mesons in each rocket will appear to have a different lifetime to the inertial observer compared to the proper lifetime. However, the proper lifetime of the mesons is the same in both rockets, which is given in the question as 2.6 × 10^-⁸ s. To determine which observation is correct for the inertial observer, we need to consider the time dilation effect on the mesons' lifetime in each rocket. The proper lifetime is the time it takes for half of the mesons to decay. This means that the mesons' lifetime is dependent on their speed relative to the observer. According to the time dilation formula, the mesons' lifetime in rocket A will appear longer than the proper lifetime, while in rocket B, it will appear shorter. This is because rocket A is moving towards the observer, so time appears to be passing slower relative to the observer. For rocket B, time appears to be passing faster than the proper time due to its velocity away from the observer. Therefore, the mesons in A will take longer to decay on average than the mesons in B. This leads to the correct observation for the inertial observer as given in choice E, "On average, the mesons in A will decay before the mesons in B."

Two Rockets, a and B, Approach Each Other as Shown