SOLUTION: Due to the work of Albert Einstein and other physicists who labored on space-time relationships, it is
known that the faster an object moves the shorter it appears to become. This
Algebra.Com
Question 1043708: Due to the work of Albert Einstein and other physicists who labored on space-time relationships, it is
known that the faster an object moves the shorter it appears to become. This phenomenon is modeled by the
Lorenz Transformation where L0
is the length of the object at rest,
L
is the relative length when the object is moving at velocity
v
, and
c
is the speed of light. Factor the radicand and use the result to determine the relative length of a domestic shorthair
cat of length 18 inches if it is shot past a stationary observer at 0.75 times the speed of light.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The length contraction (L) is calculated from the following formula
:
L = Lo / ( 1 / square root(1 - (v^2 / c^2)) ) where c is the speed of light
:
L = 1.5 / ( 1 / square root( 1 - ((7.37e8)^2 / (9.82e8)^2) )
:
note that Lo = 18 inches = 1.5 feet,
:
c = 186,000 miles per second =
186000 times 5280 (feet in a mile) = 9.82e8 feet per second,
:
(3/4) times 9.82e8 = 7.37e8 feet per second
:
***************************************************************************
L = 1.5 / (1 / square root (1 - 0.5625)) = 1.5 / (1 / 0.6614) = 0.9921 foot
The relativistic length of the cat is approx 0.9921 foot or 11.9 inches
***************************************************************************
:
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