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Speed of light is 40mph. Time Dilation and Length Contraction

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py300
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Apr28-10, 09:40 AM
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1. The problem statement, all variables and given/known data

Suppose that the speed of light in a vacuum ( c), instead of being a whooping 3x108, was a rather sluggish 40.0 mph. How would that affect everyday life? Throughout this problem we are going to assume that c = 40.0 mph and that time dilation is in full effect. Let's start by assuming that it is fairly easy to accelerate to speeds close to 40.0 mph. We will also ignore gravity throughout this problem. Otherwise, the earth (with an escape velocity of 11km/s) would have turned into a black hole long ago.

A) Suppose that a bored student wants to go to a restaurant for lunch, but she only has an hour in which to go, eat, and get back in time for class. Considering that it usually takes about 30 minutes in most restaurants to get served and to eat, what is the farthest restaurant the student can go to without being late for class? Assume in this part that the student has a car that can accelerate to its top speed in a negligible amount of time. Also, the local speed limit is 30 mph and the student would not like to get a speeding ticket.

B) The restaurant the student likes to go to doesn't have any clocks. As a result, the only way that the student can keep track of the time so as not to be late is to keep an eye on her wristwatch. According to the student's watch, how much time does she actually have for lunch if she wants to go to the furthest restaurant (including travel time)?

C) Now, suppose the student wishes to bring back some ice cream from the restaurant for her friends at school, but since it is such a hot day, the ice cream will melt away in the car in only 5 minutes. How fast will the student have to drive back to get the ice cream to her friends before it completely melts?

2. Relevant equations

T=t'/√(1-v^2/c^2)
L=L'√(1-v2/c2)

3. The attempt at a solution

I've only used time dilation and length contraction once, and I don't really get it. Can someone help me?
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