SOLUTION: Hi Can I have some help with this problem? According to the Theory of Relativity, the length L of an object is a function of its velocity v with respect to an observer. For an o

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Question 126006: Hi Can I have some help with this problem?
According to the Theory of Relativity, the length L of an object is a function of its velocity v with respect to an observer. For an object whose length at rest is 25 m, the function is given below, where c is the speed of light.
L(v)=25 sqrt(1-(v^2)/(c^2))
(a) Find L(0.5c), L(0.8c), and L(0.84c).
L(0.5c) =
L(0.8c) =
L(0.84c)=

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
L%28v%29=25+sqrt%281-%28v%5E2%29%2F%28c%5E2%29%29+

(a) Find L%28+0.5c+%29

L%280.5c+%29=25+%28sqrt%281-%28%280.5c%29%5E2%29%2F%28c%5E2%29%29%29%29+

L%280.5c+%29=25+%28sqrt%281-%28%280.5%5E2%28c%29%5E2%29%2F%28c%5E2%29%29%29%29+



L%280.5c+%29=25+%28sqrt%281-%280.5%5E2%29%29%29+

L%280.5c+%29=25+%28sqrt%281-%280.25%29%29%29+

L%280.5c+%29=25+%28sqrt%28.75%29%29+

L%280.5c+%29=25+%28.87%29+

L%280.5c+%29=21.75


b) L%28+0.8c+%29:

L%280.8c+%29=25+%28sqrt%281-%28%280.8c+%29%5E2%29%2F%28c%5E2%29%29%29%29+

L%280.8c+%29=25+%28sqrt%281-%28%280.8%5E2%28c%29%5E2%29%2F%28c%5E2%29%29%29%29+



L%280.8c+%29=25+%28sqrt%281-%280.8%5E2%29%29%29+

L%280.8c+%29=25+%28sqrt%281-%280.64%29%29%29+

L%280.8c+%29=25+%28sqrt%28.36%29%29+

L%280.8c+%29=25+%28.6%29+

L%280.8c+%29=15


c) L%28+0.84c%29:

L%280.84c%29=25+%28sqrt%281-%28%280.84c+%29%5E2%29%2F%28c%5E2%29%29%29%29+

L%280.84c%29=25+%28sqrt%281-%28%280.84+%5E2%28c%29%5E2%29%2F%28c%5E2%29%29%29%29+



L%280.84c%29=25+%28sqrt%281-%280.84%5E2%29%29%29+

L%280.84c%29=25+%28sqrt%281-%280.91652%29%29%29+

L%280.84c%29=25+%28sqrt%28.08348%29%29+

L%280.84c%29=25+%28.29%29+

L%280.84c%29=7.25