17.6 Motion’s Effect on Space: Mathematical Form

Problem

Module 17: Motion's Effect on Space: Mathematical Form - Problem 2

Imagine you are on a platform as a train rushes by with speed $v$ . You notice that someone on the train is holding a meter stick in the horizontal position and rotates it toward the vertical.

Question 1 of 2

1. Question
When the person on the train claims that the meter stick is midway between horizontal and vertical, i.e. that it makes an angle of $\pi/4$ with the horizontal axis, what angle do you say the stick makes with the horizontal axis?
- 1. $\pi/4$
- 2. $\tan^{-1}(v/c)$
- 3. $\sin^{-1}\left({ 1 \over \sqrt{1 - (v/c)^2} }\right)$
- 4. $\tan^{-1}\left({ 1 \over \sqrt{1 - (v/c)^2} }\right)$
Correct

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Question 2 of 2

2. Question
When the person on the train claims that the meter stick makes an angle of $\phi$ with the horizontal axis, what angle do you say the stick makes with the horizontal axis?
- 1. $\tan^{-1}\left( \tan(\phi) { \frac{1}{\sqrt{1 - (v/c)^2}} }\right)$
- 2. $\sin^{-1}\left( \tan(\phi) { \frac{1}{\sqrt{1 - (v/c)^2} }}\right)$
- 3. $\tan^{-1}(v/c)$
- 4. $\tan^{-1}\left( \sin(\phi) { \frac{1}{\sqrt{1 - (v/c)^2} }}\right)$
Correct

Incorrect

Module 17: Motion's Effect on Space: Mathematical Form - Problem 2

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