18.6 Length Contraction: Examples

Problem

Length Contraction: Examples - Problem 1

Imagine that you travel to the planet Zaxtar, which is 100 million light-years away as measured by astronomers on Earth, and you get there in 1 year according to your ship’s clock. Let’s work out some key details of your trip.

Question 1 of 2

1. Question
If you travel at constant speed $v$ (you'll work out the value of $v$ in just a moment), how far according to the ship's odometer is your journey?
- 1. $100,000,000$ light-years
- 2. $(100,000,000)(\sqrt{1 - (v/c)^2})$ light-years
- 3. $(100,000,000)$ $1 \over (\sqrt{1 - (v/c)^2})$ light-years
- 4. $(100,000,000) {1 \over (1 - (v/c)^2)}$ light-years
Correct

Incorrect
Question 2 of 2

2. Question
To cover the distance you calculated in part (A) in one year, what must be the value of $v$ ?
- 1. $\sqrt{ 10^{8} \over 10^{8} + 1} c$
- 2. $\sqrt{ 10^{16} +1 \over 10^{16}} c$
- 3. $\sqrt{ 10^{16} \over 10^{16} + 1} c$
- 4. $\sqrt{ 10^{16} \over 10^{16} + 10^8} c$
Correct

Incorrect

Length Contraction: Examples - Problem 1

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