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

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SUMMARY

The discussion focuses on calculating the angle theta (θ) from the angle alpha (α) using the relationship Tan(θ) = Cot(α). Participants express confusion regarding the book's assertion that θ equals α, suggesting that this is incorrect. A recommendation is made to redraw the figure using an arbitrary angle α that is not close to 45 degrees to clarify the relationship between the angles. The correct relationship derived is θ = 90 - α, which aligns with the geometric interpretation of the angles involved.

PREREQUISITES
  • Understanding of trigonometric functions, specifically tangent and cotangent.
  • Familiarity with geometric principles related to angles and velocity vectors.
  • Basic knowledge of projectile motion and impact analysis.
  • Ability to interpret and redraw geometric figures based on given conditions.
NEXT STEPS
  • Study the derivation of trigonometric identities, focusing on Tan and Cot functions.
  • Explore the principles of projectile motion and how angles affect trajectory.
  • Learn how to analyze impact angles in physics, particularly in inclined planes.
  • Practice redrawing geometric figures to visualize relationships between angles and vectors.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone involved in mechanics or kinematics, particularly those working with angles and impact analysis in inclined 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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