Question

can someone help me with this ? thanks

Tutorial Exercise The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 x 108 s. (a) If the meson moves with a s on Earth? of 0.85c, what is its mean lifetime as measured by an observer (b) What is the average distance it travels before decaying, as measured by an observer on Earth? (c) What distance would it travel if time dilation did not occur? Step 1 (a) If the proper lifetime of the pi meson is Δ, 2.6 x 10-8 s, the lifetime measured by an observer on Earth (moving at speed v 0.85c relative to the meson) is given by the following equation, where y is the factor by which the proper time interval is dilated. x 10-8 s At x 10-8 Submit Need Help? Lnnan

Answer 1

The time dilation

According to time dilation Delta t = r Delta t_p = Delta t_p/squareroot 1 - (v/c)^2 Delta t = 2.6 times 10^- 8 s/squareroot 1 - (0.8 sc/c)^2 Delta t = 2.6 times 10^- 8 s/squareroot 1 - (0.85)^2 Delta t = 4.94 times 10^- 8 s