Virginia Tech > College of Science > Physics Dept > Tatsu Takeuchi > Special Relativity > Practice Problems > Problem 4
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The Hare and the Tortoise 2

The hare and the tortoise decide to have another race. They start from the same point and race in the same direction, but the hare decides to give the tortoise a handicap by letting him race only half the distance as shown in the figure. The race takes place and the referee, who is at rest with respect to the ground, sees both animals cross their respective finish lines at the same time. The trajectory of the hare and the tortoise are shown on the space-time diagram. Answer the following questions:

  1. At which of the points labeled A through G in the space-time diagram does the hare cross its finish line?
  2. At which point does the tortoise cross its finish line?
  3. At which point is the tortoise when the hare crosses its finish line in the hare frame?
  4. At which point is the hare when the tortoise crosses its finish line in the tortoise frame?
  5. What is the result of the race in the respective frames of the hare and the tortoise? Do they agree or disagree? If they disagree, explain why it is not a contradiction.
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