A beam of unstable particles emerges from the exit slit of an accelerator with a speed of 0.89c. Particle detectors 3.0 and 6.0 m from the exit slit measure beam intensities of 2 × 10⁸ particles/cm² · s and 5 × 10⁷ particles/cm2·s, respectively.

(a) Find the proper half-life of the particles.

(b) Determine the beam intensity at the exit slit of the accelerator.

(c) The accelerator is adjusted so that the particles emerge from the exit slit with a speed of 0.96c. The beam intensity at the farther detector is again 5 × 10⁷ particles/cm²·s. Find the beam intensity at the exit slit of the accelerator.