Spring Problem: Calculate Horizontal Distance of Ball Bearing

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To solve the problem of calculating the horizontal distance traveled by a ball bearing launched from a spring at a 29-degree angle, energy analysis is suggested as the best approach. The ball bearing reaches a height of 1.41 meters, which can be used to determine its initial velocity upon release. By calculating the velocity of the ball bearing when dropped from that height, the horizontal and vertical components of the velocity can then be derived using trigonometric functions. The horizontal distance can be found by applying projectile motion equations based on these components. Understanding the conversion of potential energy to kinetic energy is crucial for this calculation.
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Homework Statement



A small steel ball bearing with a mass of 29.0 g is on a short compressed spring. When aimed vertically and suddenly released, the spring sends the bearing to a height of 1.41 m. Calculate the horizontal distance the ball would travel if the same spring were aimed 29.0o from the horizontal.


The Attempt at a Solution



Ok so I know that F = -kx but I don't get k or x in this problem. So I can' use that. I am not really sure where to start with this problem. Do I use F = ma? I still wouldn't be able to get its initial velocity out of that.
 
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The easiest way to do this problem would be to use energy analysis, do you know how to do that?
 
how fast would an object dropped from a height of 1.4 meters be going. now find the horizontal and vertical components of that velocity if aimed at 29 degrees.
 

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