1. A friend in a spaceship travels past you at a high speed. He tells you that h

Question

1. A friend in a spaceship travels past you at a high speed. He tells you that his ship is 24 m long and that the identical ship you are sitting in is 19 m long.

(a) According to your observations, how long is your ship?
?m
(b) According to your observations, how long is his ship?
?m
(c) According to your observations, what is the speed of your friend's ship?
?c

2. The proper length of one spaceship is three times that of another. The two spaceships are traveling in the same direction and, while both are passing overhead, an Earth observer measures the two spaceships to have the same length. If the slower spaceship is moving with a speed of 0.39c, determine the speed of the faster spaceship.
?c

Explanation / Answer

a) Since your ship is identical to your friend's, it must have the same proper length. The proper length of his ship is 24m, so that must be the proper length of your ship.

b) Your friend, moving with speed v relative to you, measures your 24m ship to be 19m long. You are moving with speed v relative to your friend, so you will measure his 24m long ship to be 19m long as well.so answer will be 19m.

c)

V= sqrt(1-192/242)
V= .3733c = 1,11,990 km/s

d) Gamma1 = 1 / sqrt( 1 - (0.39)2 )
Gamma2 = 3 * Gamma1 = 1 / sqrt( 1 - (v/c)^2 )

Gamma1 = 1.085994
Gamma2 = 3.257983

sqrt( 1 - (v/c)2 ) = 1 / Gamma2
1 - (v/c)2 = 1 / Gamma22
(v/c)2 = 1 - 1 / Gamma22
v/c = sqrt( 1 - 1 / Gamma22 )
v = sqrt( 1 - 1 / Gamma22 ) * c
v = 0.9517c

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