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

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To find the height required for a bead to reach a velocity of 4.5 m/s at the lowest point on a frictionless wire, conservation of energy indicates a height of approximately 1.033 m. The discussion then shifts to determining the angle that minimizes the time to achieve this velocity. The contributor suggests that the optimal angle would maximize vertical acceleration, but struggles to identify the specific angle. Clarification is sought on how to approach this second part of the problem. The conversation emphasizes the relationship between height, velocity, and angle in the context of physics principles.
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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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