A spaceship passes you at a speed of 0.85c. You measure its length to be 28.2 m.

Question

A spaceship passes you at a speed of 0.85c. You measure its length to be 28.2 m. How long would it be when at rest? A certain type of elementary particle travels at a speed of 2.82 times 10^8 m/s. At this speed, the average life-time is measured to be 4.09 times 10^-6s. What is the particle's lifetime at rest? If you were to travel to a star 93 light-years from Earth at a speed of 2.8 times 10^8m/s, what would you measure the distance to be? What is the speed of pion if its average lifetime is measured to be 2.79 times 10^-8 s? At rest, its average lifetime is 4.3 times 10^-8 s. In an Earth reference from, a star is 82 light-years away. How fast would you have to travel so that, to you, the distance would be only 35 light-years.

Explanation / Answer

1) Length of spaceship at rest is given by.

Lo = L/(1- v2/c2)1/2 = 28.2/(1- 0.852)1/2 = 53.53 m

2) Lifetime at rest is,

to = t*(1- v2/c2)1/2 = 4.09*10-6*{1- (2.82/3)2}1/2 = 1.4*10-6 s

3) distance measured,

d= (1- v2/c2)1/2 * do = 93*{1- (2.8/3)2}1/2 = 31.62 light-year

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