Potential barrier problem in mechanics

[Rhdjfgjgj]

Homework Statement

Question:find minimum velocity so that the ball reaches A,B, and C .in the given figure

Relevant Equations

Energy conversion equation

Here our sir said if I would apply energy conservation b/w initial point and B , we would get it wrong. But If I apply between initial point and D , we would get it right. He didn't tell why. Could anyone just explain why. One reason I thought was that since the question asked for minimum velocity and since D is a point of unstable equilibrium just giving enough velocity to get it past D is sufficient

 

[hutchphd]

According to the diagram the initial point is at E. To get to B the ball must traverse D. The fact that B is lower than D does not matter according to classical mechanics. Mechanical energy must be conserved at every point along the path.
Quantum mechanics gives a slightly more nuanced answer.

 

[Lnewqban]

... One reason I thought was that since the question asked for minimum velocity and since D is a point of unstable equilibrium just giving enough velocity to get it past D is sufficient

I believe that your reasoning is correct.
Initial velocity at E should be the maximum minimum value that the ball will need to have to hit points A, B and C.

Edit: See post 4.

 

[hutchphd]

Initial velocity at E should be the maximum value that the ball will need to have to hit point A

I do not undertstand what this means. Why is there a maximum limit??

 

[hutchphd]

@Lnewqban and @Rhdjfgjgj I think the problem seeks a calculated value for $v_0$ not the ensuing values at various points on the course. Am I misreading it?

 

[Lnewqban]

I do not undertstand what this means. Why is there a maximum limit??

Correction appreciated.
Post 3 edited.