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## Homework Statement

A spaceship travels past a planet at a speed of 0.80 c as measured from the planet’s frame of reference. An observer on the planet measures the length of a moving spaceship to be 40 m.

a) How long is the spaceship, according to the astronaut?

b) At what speed would the spaceship have to travel for its relativistic length to be half its “proper” length?

## Homework Equations

L= Lo x [tex]{\sqrt{1 - \frac{ v^2 }{ c^2 }}}[/tex]

## The Attempt at a Solution

a)

Lo=40m

v=0.80c

Using the equation above I came to a answer of L = 24m

b)

L= 0.5 Lo

0.5Lo = Lo x [tex]{\sqrt{1 - \frac{ v^2 }{ c^2 }}}[/tex]

v^2 = (0.75)(c^2)

v= Square root [(0.75)(c)]

c= 3.0x10^8

v= 15000 m/s

The speed of the spaceship must be 15000 m/s.

Could someone verify this? The 15,000 m/s seems small.