Calculating theta from alpha: Tan(theta)=Cot(alpha)

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Homework Help Overview

The discussion revolves around calculating the angle theta in relation to another angle alpha, specifically through the relationship Tan(theta) = Cot(alpha). Participants are examining the implications of this relationship in the context of a physics problem involving impacts and inclined planes.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are attempting to derive theta from the given relationship and questioning the validity of the book's assertion that theta equals alpha. They explore geometric interpretations and consider the implications of the angles involved before and after impact.

Discussion Status

There is an ongoing exploration of the relationship between the angles, with some participants suggesting that the book may be incorrect. Questions are raised about the angles made by velocity with the inclined plane and how these relate before and after impact. Multiple interpretations of the angle measurement are being discussed, indicating a productive dialogue.

Contextual Notes

Participants note that the book's answer may not hold true for arbitrary angles and suggest redrawing figures for clarity. There is also mention of the ambiguity in measuring angles from different reference planes.

Shivam
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Homework Statement
The angle theta with the inclined plane which the velocity makes just after 1st impact will be ?
Relevant Equations
Conservation of linear Momentum. Coefficient of restitution.
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After impact VCos(alpha) will be normal to the inclined, now i calculated for theta by using [ Tan(theta) = vCos(alpha)/vSin(alpha),. Tan(theta)= Cot(alpha) ]. I don't know how to solve further to get value of theta, according to book thta = alpha.
 
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Shivam said:
I don't know how to solve further to get value of theta, according to book thta = alpha.

The answer fron the book is incorrect. However, the way figure is drawn may make it appear to be correct. Since the result has to work for an arbitrary angle ##\alpha##, I suggest that you redraw the figure using a value of ##\alpha## that is not so close to 45 deg.

Try answering these questions; they should make the correct solution clear:
- What angle will the velocity make with the plane before impact?
- How will the velocity after impact be related to the velocity before impact?
 
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tnich said:
The answer fron the book is incorrect. However, the way figure is drawn may make it appear to be correct. Since the result has to work for an arbitrary angle ##\alpha##, I suggest that you redraw the figure using a value of ##\alpha## that is not so close to 45 deg.

Try answering these questions; they should make the correct solution clear:
- What angle will the velocity make with the plane before impact?
- How will the velocity after impact be related to the velocity before impact?
Bro , i thought geometrically and angle was not equal to alpha , i also tried this [ Tan(theta) = Cot(alpha),
Tan(theta) = Tan(90-alphal),
So, theta = 90 - alpha],
is it correct
 
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Shivam said:
Bro , i thought geometrically and angle was not equal to alpha , i also tried this [ Tan(theta) = Cot(alpha),
Tan(theta) = Tan(90-alphal),
So, theta = 90 - alpha],
is it correct
Looks right to me, though it seems (4) should also be valid since the question does not indicate whether the angle is to be measured from the half plane below impact or from the half plane above it.
 
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