**Part A**

The officer sees the contracted length of the spaceship.

This length is given by:

$\overline{){\mathbf{L}}{\mathbf{=}}{{\mathbf{L}}}_{{\mathbf{0}}}\sqrt{\mathbf{1}\mathbf{-}\frac{{\mathbf{v}}^{\mathbf{2}}}{{\mathbf{c}}^{\mathbf{2}}}}}$

From the graph we can use:

$\mathit{L}\mathbf{=}\sqrt{\mathbf{1}\mathbf{-}\frac{{\mathbf{v}}^{\mathbf{2}}}{{\mathbf{c}}^{\mathbf{2}}}}$, for a particular v.

Label the spaceships as follows:

(1) L = (100)(0.6) = 60 m

(2) L = (200)(0.9) = 180 m

(3) L = (100)(0.9) = 90 m

Six spaceships with rest lights L_{0} zoom past an intergalactic speed trap. The officer on duty records the speed of each ship , v. (No ship is going in excess of the stated speed limit of c, so she doesn't have to pull anyone over for a ticker.)

Part A.

Rank these spaceships on the basis of their length measured by the police officer.

Part B

Rank these spaceships on the basis of their lengths as measured by their respective captains.

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