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- Homework Statement
- A hollow cone is placed on the ground like shown in example. Inside a cone there is string attached to base center. In the string there is a small bead. What must the angle between string and vertical be, so bead reaches cone surface fastest? (You can stretch the string). Cone base is parallel to the ground and cone has angle φ. String frictionless.

- Relevant Equations
- kinematic eqs

trig identites

I tried to come up with expression of time in terms of φ, α, and some constant value of cone size that does not depend on angle (I used R as cone radius). I though I could use that expression to see at what angle time is going to minimum, but I came up with expression from which I can't make a conclusion. I believe there is another solution method, or maybe there are some useful trig identities, but I was unable to find it.

Can someone help me out? Thanks

Angle φ is marked badly at my solution, but that doesn't change anything in particular.

Can someone help me out? Thanks

Angle φ is marked badly at my solution, but that doesn't change anything in particular.