QuestionJune 21, 2025

Question 3(Multiple Choice Worth 1 points) (06.09 MC) A clock moves past you at a speed of 0.9 c. How much time passes for you for each second that elapses on the moving clock? 0.436 s 1.15 s 2.29 s Infinity

Question 3(Multiple Choice Worth 1 points) (06.09 MC) A clock moves past you at a speed of 0.9 c. How much time passes for you for each second that elapses on the moving clock? 0.436 s 1.15 s 2.29 s Infinity
Question 3(Multiple Choice Worth 1 points) (06.09 MC) A clock moves past you at a speed of 0.9 c. How much time passes for you for each second that elapses on the moving clock? 0.436 s 1.15 s 2.29 s Infinity

Solution
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Answer

2.29 s Explanation 1. Identify the formula for time dilation Use the time dilation formula: **t' = \frac{t}{\sqrt{1 - \frac{v^2}{c^2}}}** where t' is the time observed in the stationary frame, t is the proper time, v is the velocity of the moving clock, and c is the speed of light. 2. Substitute values into the formula Given v = 0.9c, substitute into the formula: t' = \frac{1}{\sqrt{1 - (0.9)^2}}. 3. Calculate the time dilation factor Compute \sqrt{1 - (0.9)^2} = \sqrt{1 - 0.81} = \sqrt{0.19}. 4. Solve for t' t' = \frac{1}{\sqrt{0.19}} \approx 2.29 seconds.

Explanation

1. Identify the formula for time dilation<br /> Use the time dilation formula: **$t' = \frac{t}{\sqrt{1 - \frac{v^2}{c^2}}}$** where $t'$ is the time observed in the stationary frame, $t$ is the proper time, $v$ is the velocity of the moving clock, and $c$ is the speed of light.<br />2. Substitute values into the formula<br /> Given $v = 0.9c$, substitute into the formula: $t' = \frac{1}{\sqrt{1 - (0.9)^2}}$.<br />3. Calculate the time dilation factor<br /> Compute $\sqrt{1 - (0.9)^2} = \sqrt{1 - 0.81} = \sqrt{0.19}$.<br />4. Solve for $t'$<br /> $t' = \frac{1}{\sqrt{0.19}} \approx 2.29$ seconds.
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