Question

The USS Enterprise passes a star system at a sub-light speed of (2.00 × 10⁸ , m/s). Inhabitants of that system measure the length of the spaceship at 540 m. What is the length of the spaceship according to its passengers?

a) (540 , m)
b) (2.00 × 10⁸ , m)
c) (√540² + (2.00 × 10⁸)² , m)
d) (540 × 2.00 × 10⁸ , m)

Answer 1

The length of the spaceship as measured by an Earth-bound observer is 536.76 m.

Step-by-step explanation:

In special relativity, there is a phenomenon called length contraction which states that objects moving at high speeds appear shorter in the direction of their motion when observed from a stationary frame of reference. The formula for length contraction is l' = l0 / √(1 - v²/c²), where l' is the contracted length, l0 is the proper length, v is the relative velocity, and c is the speed of light. In this scenario, the spaceship is moving at a speed of 0.970c and its proper length is 200 m. Therefore, the length of the spaceship as measured by an Earth-bound observer would be l' = 200 / √(1 - 0.970²) = 536.76 m.