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Problem:

(1) In relativity theory, the length of an object (for example a rocket) appears to an observer to depend on the speed at which the object is traveling with respect to the observer. If the observer measures the rocket’s length as at rest, then at speed v, the length will appear to be L=L0 √(1-(v²/c²))

where c is the speed of light in a vacuum, about 3 x 10^8 m/sec.

(a) What happens to L as v increases?

(b) Find Lim L as v approaches c-
(c) Why was the left hand limit needed?

ii) Given the above problem, provide written responses to address the following points as precisely and thoroughly as possible.

(1) Explain the problem.

(2) What mathematical concepts apply to this problem?

(3) Explain the steps taken to solve the problem.

(4) What is the most difficult aspect of solving this problem?

(5) Explain exactly what the answer means from a mathematical perspective.

We won't do your homework for you, however we will help if you show a goofd faith attempt to answer it yourself. For example, in part a, as v increases toward c, can you see that v/c approaches 1? Don't forget that v can never quite equal c, and certainly can't exceed it. What happens to L_0 \sqrt {1 - \frac {v^2} {c^2} } as \frac v c approaches 1 (but doesn't exceed it)?