Plz help with physics! I will give best answer vote to who can answer most!?

Question

1. What are the limits on the minimum and maximum values for the Lorentz factor?

2. At what speed would a clock be moving so that time dilation would cause it to run slow by 50%?

3. A spaceship observed from Earth to be moving toward a star at a speed of 0.80 c. If distance from spaceship to star is 1.6 ly as measured from Earth, how long does an observer on Earth find that it takes for ship to reach the star?

4. A spaceship observed from Earth is moving toward a star at speed .80 c and distance still 1.6 ly, how far is star as measured from moving spaceship?

5.Radioactive particles moving at .80 c measured to have half-life of 4.3 x 10^ -8 s. What is their half-life when at rest?

6. Two cars traveling in same direction. Car A going 30 m/s and B passing A at relative speed of 3.0 m/s. What is speed of B?

7. In same situation as #6, using Galilean realitvity to calculate speed of car B relative to highway results in answer incorrect by how many m/s?

Answer 1

1. The Lorentz factor starts out at 1 for zero relative velocity and approaches infinity when the relative velocity approaches the speed of light.

2. That would be 1/2 = √(1 − (v/c)²).  This equation will be true when v/c = ±√3 / 2.

3.  I won't actually do the math, but the Lorentz factor γ will be exactly 5/3 for a speed 4/5 the speed of light.  Because both speed and distance are measured from the same point of reference, you can still use the old-fashioned d = rt, for a travel time of 2.0 years to the star.

4. However, the space ship sees the distance to the star contracted to 3/5 of the distance as seen from earth, or 0.96 ly.

5. The time dilation factor for 0.80c is 5/3, so the particles' half-lives observed in a frame in which the particles are at rest will be reduced the reciprocal of the dilation factor of the lab frame, or 3/5.  The particles therefore have a half-life of 3/5*4.3e-8 s or 2.6e-8 s in their own rest frame.

6. Taking the liberty of using Galilean relativity, car B is traveling at 33.0 m/s with respect to the road.

7. I forget how to do this calculation exactly, but the error will be somewhere on the order of ½(v/c)², or about 5e-15.  Even NIST would be unable to tell the difference between Einsteinian and Galilean results at these speeds.