# Relativity

alexjlaonnae | 18:36 Wed 29th Jan 2014 | Science
On the ground a spaceship measures 25 m in length. Later in the day Isaac goes to space. After the spaceship reaches cruise speed, Albert find that its length has contracted to 10 m. What is the speed of the spaceship?

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The speed of light x (25 - 10)/25
Isaac will also have contracted in the direction of travel and will probably be feeling too unwell to measure his spaceship.
Issac will not know his space ship has shrunk, both he and the tape measure will have shrunk as well, to him it will look and measure up at just the same size.
10 m/25 m = 0.4 meters
-------------------------

0.4 * 2.998 X 10^8 m/s

= 1.199 X 10^8 meters per second
==========================
There was a young lady called Wright, who could travel much faster than light.
She went out one day in a relative way and came back the previous night.
I presume the question assumes Albert is still on the ground?
Not sure why people are just taking the ratio of the two lengths -- the relationship is given by a Lorentz factor 1/Sqrt[1-(v^2)/(c^2)], so that a contraction of 25m to 10 m gives a speed of:

Contracted Length = Original Length / Lorentz factor

10=25/(1/Sqrt[1-(v^2)/(c^2)])

10/25= Sqrt[1-(v^2)/(c^2)]

(10/25)^2=[1-(v^2)/(c^2)]

(10/25)^2= 1-(v^2)/(c^2)

(v^2)/(c^2)=1-(10/25)^2

v/c=Sqrt[1-(10/25)^2]

v=c*Sqrt[1-(10/25)^2]

v=c*Sqrt[1-0.4^2]

v=c*Sqrt[1-0.16]

v=c*Sqrt[0.84]

v=c*0.9165...

v=299792458*0.9165...

v=274,764,326 m/s (or about 275 million metres per second, or just 0.92*c).
Quite quick then^^^?
I can run faster than that .... when they call last orders at my local :P

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