How to find out the range of a spring?

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To determine the range of a spring, first calculate the spring constant and initial velocity using projectile motion equations. The conservation of energy can then be applied, where the potential energy stored in the spring (½ kx²) equals the kinetic energy (½ mv²). This allows for the calculation of the necessary stretch (x) of the spring to achieve a desired launch distance. Utilizing these physics principles provides a comprehensive method for finding the spring's range. Understanding both projectile motion and energy conservation is essential for accurate calculations.
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How to find out the range of a spring??

I need to find the range of a spring after finding the spring constant. I have reduced the formula after using conservation of energy concepts and projectile motion. Is there another way to find out how much you need to stretch the spring to launch it a certain distance? Thanks
 
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Well you can use projectile motion equations such as range to get the initial velocity v and then use conservation of energy

½ kx2 = ½ mv2 to get x.
 

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