An unstable particle called Bullroarium has a lifetime of 6x10E-10 seconds, measured at rest. If a Bullroariom particle zips past a stationary observer at 0.67c , find the stationary observer’s measurements for

A.) Bullroarium lifetime as measured by the stationary observer and
B.) The distance it travels during this time as measured by the stationary observer.

To answer these questions, we'll need to use the concepts of time dilation and length contraction from special relativity.

A.) To find the stationary observer's measurement of the Bullroarium lifetime, we need to apply time dilation. Time dilation states that time appears to pass more slowly for objects moving relative to an observer. The formula for time dilation is:

t' = t / (γ)

Where t' is the observed time, t is the time in the rest frame of the particle, and γ (gamma) is the Lorentz factor given by:

γ = 1 / √(1 - (v^2 / c^2))

In this case, the rest frame lifetime of the Bullroarium particle is 6x10^-10 seconds. The velocity of the particle relative to the stationary observer is 0.67c. Therefore, we need to find the Lorentz factor (γ) first:

γ = 1 / √(1 - (0.67c)^2 / c^2)
≈ 1.56

Now, we can calculate the observed lifetime (t'):

t' = (6x10^-10 seconds) / (1.56)
≈ 3.85x10^-10 seconds

Thus, the stationary observer measures the Bullroarium particle's lifetime to be approximately 3.85x10^-10 seconds.

B.) To find the distance traveled by the Bullroarium particle as measured by the stationary observer, we need to consider length contraction. Length contraction states that the length of an object appears shorter when it is in motion relative to an observer. The formula for length contraction is:

L' = L * γ

Where L' is the observed length, L is the rest length of the particle, and γ (gamma) is the Lorentz factor.

In this case, since the particle's rest frame length is not given, we can assume it's negligible (e.g., it's a point-like particle). Therefore, the observed distance traveled by the particle (L') would be:

L' = 0 * γ
= 0

This means that the stationary observer measures the distance traveled by the Bullroarium particle to be zero.