physics quuestions

Problem Set 3 Kleiban 1. A rocket (in frame S’) is moving at a speed v = 4c/5 relative to the moon (frame S). At t0 = 2×10−7 s a UFO appears at a point x0 = 10m traveling in the x0 direction with constant velocity u0 = −c/2. It suddenly dissappears at t0 = 2.5×10−7 s. As measured by someone on the moons surface, (a) What was the velocity of the UFO? (b) How far did it travel? 2. Three identical radio transmitters A, B and C each transmitting at the frequency νo in its own rest frame are in motion as shown (a) What is the frequency of B’s signals as measured by C? (b) What is the frequency of A’s signals as measured by C? 3. Consider three galaxies A, B and C. An observer in A measures the velocities of C and B and finds they are moving in opposite directions each with a speed of 0.7c relative to him. Thus according to measurements in his frame the distance between them is increasing at the rate 1.4c. (a) What is the speed of A observed in B? (b) What is the speed of C observed in B? 4. A K o -meson (elementary particle) at rest decays into a π + and π − meson each having a speed of 0.85c. If a K o meson travelling at a speed of 0.9c decays (a) What is the greatest speed that one of the π mesons can have? (b) What is the least speed? 5. Show that the relativistic expression for kinetic energy reduces to the classical result when v