QQuestionPhysics
QuestionPhysics
A star is 40 light-years from Earth. If you traveled to it at 0.995 c, how long would the trip take you?
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Step 1:I'll solve this problem step by step, carefully following the LaTeX formatting guidelines:
Step 2:: Identify the Given Information
- Distance to star: $$40 \text{ light-years}
- Travel speed: 0.995c (where c is the speed of light)
Step 3:: Understand Time Dilation
- $$c$$ is the speed of light
Due to relativistic effects, the time experienced by the traveler (proper time) will be different from the time measured on Earth. We'll use the time dilation formula: Where:
Step 4:: Calculate Time Dilation Factor
\gamma = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{1}{\sqrt{1 - (0.995)^{2}}} \approx 10.13
First, calculate the time dilation factor:
Step 5:: Calculate Travel Time
Proper time experienced by traveler: $$t_{0} = t \div \gamma = 40.20 \div 10.13 \approx 3.96 \text{ years}
Final Answer
- Time measured on Earth: 40.20 \text{ years} - Time experienced by traveler: 3.96 \text{ years}
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