A rocket of rest length 100 meters is moving at 0.6c relative to earth and conta

Question

A rocket of rest length 100 meters is moving at 0.6c relative to earth and contains an astronaut at the tail end of the ship. The astronaut fires a bullet toward the front of the ship. The velocity of the bullet relative to the astronaut is 0.8c.

(a)

How fast does the bullet move with respect to earth observers?

(b)

What is the length of the ship according to the astronaut? To earth observers? To the observers moving with the bullet?

(c)

How much time does it take the bullet to reach the front of the ship as measured by earth observers? As measured by astronauts at rest with respect to the ship? As measured by observers moving with the bullet?

Explanation / Answer

apply the relativistic considerations

v = u'+v/(1 + u'v/c^2)

v = (0.6+0.8)/{(1+ (0.6* 0.8))}

v = 0.945 c

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apply lorentz factor gamma = 1/(sqrt(1-v^2/c^2)

so Gamma = 1/(sqrt(1 - 0.6^2)

gamma = 1.25

so

Length contraction L = Lo/gamma

L = 100/1.25

L = 80 m to the observer on earth

gamma g = 1/sqrt (1- 0.8^2)   = 1.67

L = 100/1.67 = 60 m

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t earth = 0.6c/80 = 2.25 e6 secs

t bullet = 0.8c/60 =   4e6 secs

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