Example from Physics, 10.2 Consequences of Special Relativity

The Speed of Light

One night you are out looking up at the stars and an extraterrestrial spaceship flashes across the sky. The ship is 50 meters long and is travelling at 95 percent of the speed of light. What would the ship’s length be when measured from your earthbound frame of reference?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
List the knowns and unknowns.

Knowns: proper length of the ship, L₀ = 50 m; velocity, v, = 0.95c

Unknowns: observed length of the ship accounting for relativistic length contraction, L.

Choose the relevant equation.

$L = \frac{L_{0}}{γ} = L_{0} \sqrt{1 - \frac{u^{2}}{c^{2}}}$
Solution
$L = 50 m \sqrt{1 - \frac{{(0.95)}^{2} c^{2}}{c^{2}}} = 50 m \sqrt{1 - {(0.95)}^{2}} = 16 m$

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Strategy

Solution

Strategy

Solution