What is the Speed of a Block After Traveling 0.9 m Up an Inclined Plane?

AI Thread Summary
A block of mass 1 kg is placed on a spring with a constant of 500 N/m at the bottom of a frictionless inclined plane angled at 30°. When released, the block travels 1.5 m up the plane, and the problem asks for its speed after traveling 0.9 m. The user attempted to apply the work-energy principle but encountered issues with obtaining results that fit the multiple-choice options. There is confusion regarding the use of the angle in calculations and how to properly format equations in the forum. Proper formatting can be achieved using the site's editing tools or LaTeX syntax for clarity in posts.
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Homework Statement


I have run across another problem while reviewing for finals that I am not able to really understand, and this one I have no clue how to approach. I am given that a block is of mass 1 kg, it is placed on a spring of constant 500 N/m at the bottom of a frictionless plane inclined at 30°. When the spring is released the block travels 1.5 m up the plane, losing contact with the spring. What is the speed of the block when it has traveled 0.9 m up the plane?

Homework Equations


Not really sure, I tried using:
W=(1/2)kx2
and:
K=(1/2)mv2

The Attempt at a Solution


So, I tried finding the work, and then using the work in place of K to find the velocity. This returned double digit numbers, which due to the question being multi-choiced with only single digit numbers, are obviously wrong. Also, where am I supposed to use the supplied angle?
 
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On a side note, how do you format your posts so the equations look nice as you see in a lot of other posts on these boards?
 
You'll have to show your attempt in detail so that we can see what you did right and where you went wrong.

As for equation formatting, you can use the icons and menus available in the edit panel header bar for things like subscripts and superscripts and special characters (such as Greek letters) if you use plain text equations, or you can use the built-in LaTeX syntax interpretation that the website implements. This requires learning some LaTeX syntax. For more information check out the LaTeX Primer.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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