A spaceship of triangular shape,having a length three times its width,is capable of relativistic speeds.How fast would it have to move so that to a stationary observer its length would equal its width?
A)0.333c
B)0.816c
C)0.943c
D)0.650c
E)This is not possible.

Question

A spaceship of triangular shape,having a length three times its width,is capable of relativistic speeds.How fast would it have to move so that to a stationary observer its length would equal its width?
A)0.333c
B)0.816c
C)0.943c
D)​0.650c
E)​This is not possible.

Quizplus · Accepted Answer

Let the width of the spaceship be x, then its length is 3x. According to special theory of relativity, the length of an object moving with relativistic speed is contracted by a factor of gamma, which is given by:

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

where v is the velocity of the spaceship and c is the speed of light.

Now, when the spaceship is moving with a velocity v, its length along the direction of motion is contracted to x, which is equal to its width. Therefore, we have:

gamma * 3x = x

Simplifying this equation, we get:

gamma = 1 / 3

Substituting this value of gamma in the first equation, we get:

1/3 = 1 / sqrt(1 - (v^2/c^2))

Solving for v, we get:

v = 0.943c

Therefore, the spaceship would have to move at a velocity of 0.943 times the speed of light in order to appear to a stationary observer to have length equal to its width. Hence, the best choice is (C).

A Spaceship of Triangular Shape,having a Length Three Times Its