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wilson_chem90
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Homework Statement
A spaceship travels past a planet at a speed of 0.80 c as measured from the planets frame of reference. An observer on the planet measures the length of a moving spaceship to be 40m.
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 of its "proper " length?
Homework Equations
L = Lo sqrt(1 - v^2/c^2)
The Attempt at a Solution
L = Lo sqrt(1 - v^2/c^2)
= 40 m sqrt {1 - (o.80)^2/c^2}
= 40 m (0.6)
= 24 m
b) For this question I am not too sure what to do
this is all i can think of:
L = Lo sqrt(1 - v^2/c^2)
i rearranged the equation t^2 = 4L^2 / c^2 - v^2 to get v^2 = c^2/4L^2
by using this:
v^2 = (3.00 x 10^8 m/s)^2 / 4(20m)^2
= (9.0 x 10^16 m^2/s^2) / 1600 m^2
= 5.625 x 10^13
v = sqrt (5.625 x 10^13)
= 7.5 x 10^6 m/s
I am pretty sure that's not right, however, its all i can think of momentarily. Any suggestions??