A mystery spacecraft is travelling at a hidden speed v (as a fraction of light speed, v/c). All you're told is what its clock and metre-stick would look like from Earth — the dilated time and contracted length. Adjust your own spacecraft's speed until your numbers match the mystery ship's, then submit your estimate of v/c.
| Quantity | Value |
|---|---|
| Lorentz factor γ | |
| Dilated time (proper time = 10.0 s) | |
| Contracted length (proper length = 10.0 m) | |
| Relativistic mass (rest mass = 1.0 kg) |
An identical 10.0 s clock and 10.0 m rod are on board. Mission Control on Earth measures:
| Quantity | Observed value |
|---|---|
| Dilated time | |
| Contracted length |
Δt = γτ, L = L₀/γ, where γ = 1/√(1−v²/c²). Work backwards from the observed time or length to find v/c.
