A spaceship of triangular shape,having a length twice 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)0.500 c
B)0.750 c
C)0.866 c
D)This is not possible.

Question

Quizplus · Accepted Answer

According to the theory of relativity, the length of an object appears to decrease as its speed approaches the speed of light. This is known as length contraction.

Let's assume that the spaceship is moving at a speed v. Its length is given as twice the width, so if its width is w, then its length is 2w.

To a stationary observer, the length of the spaceship appears to be contracted to its width. So, we can set up the following equation:

2w*sqrt(1-v^2/c^2) = w

where c is the speed of light.

Simplifying the equation, we get:

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

Squaring both sides, we get:

1-v^2/c^2 = 1/4

v^2/c^2 = 3/4

v/c = sqrt(3)/2

v = (sqrt(3)/2)*c

This is approximately 0.866 c, which is the speed at which the spaceship would have to move so that its length would appear equal to its width to a stationary observer. Therefore, the correct answer is C.

A Spaceship of Triangular Shape,having a Length Twice Its Width,is