MHB Kinematics, time taken to a wall disappear

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The discussion revolves around a kinematics problem involving a train traveling at 3.0 m/s past an inclined wall. There is a disagreement on the time it takes for the superior face of the wall to appear and disappear through a window, with one participant calculating 3.5 seconds and another confirming the book's answer of 2.1 seconds. The calculations hinge on the wall's shape and the interpretation of the term "superior face." The participants analyze the distance traveled and the width of the train to arrive at their respective conclusions. Clarifications and further calculations are expected after a visual aid is provided.
Fantini
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I'm posting this because I disagree with the answer. Here's the question.

You are in a train that is traveling at $3.0$ m/s along a straight horizontal railroad. Very close and parallel to the railroad there exists a wall with upwards inclination of $12^{\circ}$ with the horizontal. Looking through the window ($0.9$ m tall and $2.0$ m wide) from its compartment, the train is moving to the left. The superior face of the wall appears first at edge $A$ of the window and finally disappears at edge $B$ of the window. How much time passes between the appearance and disappearance of the superior face of the wall?

The book gives the answer as $2.1$ s, but I find $3.5$ s. There is a picture but I'll have to upload it later. I'll add it to this post together with my thoughts on the problem after I sleep. :)
 
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Fantini said:
I'm posting this because I disagree with the answer. Here's the question.

You are in a train that is traveling at $3.0$ m/s along a straight horizontal railroad. Very close and parallel to the railroad there exists a wall with upwards inclination of $12^{\circ}$ with the horizontal. Looking through the window ($0.9$ m tall and $2.0$ m wide) from its compartment, the train is moving to the left. The superior face of the wall appears first at edge $A$ of the window and finally disappears at edge $B$ of the window. How much time passes between the appearance and disappearance of the superior face of the wall?

The book gives the answer as $2.1$ s, but I find $3.5$ s. There is a picture but I'll have to upload it later. I'll add it to this post together with my thoughts on the problem after I sleep. :)

After making a guess as to the shape and positioning of the wall, I'm getting $2.1\text{ s}$.
Hmm. I can also see how $3.5\text{ s}$ can come out.
It all depends on the shape of the wall and the wording superior face.

I'll explain after you add the picture and post your thoughts. (Wink)
 
I know the image is too big. Sorry about that.

The distance point $A$ travels is $d$, which is the lower side of the right triangle given by point $B$, the line drawn and the direction traveled by $A$, plus the width of the train, $2$ m. Therefore the time taken will be $$t = \frac{d+2}{v} = \frac{\frac{0.9}{\tan(12^{\circ})}+2}{3} \approx 3.5 \text{ s}.$$ I've checked and the answer given coincides with a situation where we discount the time taken to travel the width of the train, that is, $$t = \frac{d-2}{v} \approx 2.1 \text{ s}.$$ Is my interpretation correct?
HH51Mz2.png
 
Looks fine, except that I find that:

$$t = \frac{\frac{0.9}{\tan(12^{\circ})}+2}{3} \approx 2.1 \text{ s}$$

See W|A.
 
are-you-wizard.jpg


Could I have already become insane? ;) I think I typed the wrong commands in Mathematica. I'm not that bad at kinematics afterall. Thanks ILS!
 
Fantini said:
Could I have already become insane? ;) I think I typed the wrong commands in Mathematica. I'm not that bad at kinematics afterall. Thanks ILS!

Yes. I'm a wizard.
But mind you, I'm trying to keep a low profile. ;)
 
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