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

[Shivam]

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.

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.

 

[tnich]

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?

 

[Shivam]

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

 

[haruspex]

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.