Solve Bead Problem: Find Height & Angle for 4.5m/s Velocity

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SUMMARY

The bead problem involves determining the height required for a bead to achieve a velocity of 4.5 m/s at the lowest point of a frictionless wire. Using the conservation of energy principle, the calculated height is 1.033 meters. The discussion also addresses finding the optimal angle that minimizes the time to reach this velocity, focusing on maximizing vertical acceleration. Participants agree on the height calculation but seek clarification on the angle determination.

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Homework Statement


Homework Statement [/b]
Situation: bead sliding on a fristionless wire.
How large must the hieght be if the bead starting at rest is to have a velocity of 4.5m/s at the lower point? What angle will give the shortest time to achieve the correct velocity?


Homework Equations





The Attempt at a Solution


I attempted to first finding h by using the conservation of energy Potential(intial)=Kinetic(final) and i came out with 1.033m. let me know if i was right. The main problem is the second part. I'm drawing a blank to find the angle with only one component. Maybe I am missing something. Thank u in advanced
 
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i think the shortest time would be for that angle in which the acceleration along the vertical is maximum. So what would that angle be?

And I do get the same answer as you did for the first part.
 

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