Two questions, work-kinetic energy related

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The discussion revolves around two physics problems related to work and kinetic energy. The first question involves calculating the work done by friction on a 5.0-kg block sliding down a 30-degree incline with a coefficient of kinetic friction of 0.25 at a speed of 3.0 m/s. The second question concerns a 2.0-kg block sliding down a frictionless incline with an external force of 3.0 N, requiring the determination of its kinetic energy at point B, given its kinetic energy at point A is 10 J. Participants express confusion over their calculations, particularly in applying the correct equations for work and kinetic energy. Clarification and guidance on the application of the relevant physics principles are sought to arrive at the correct answers.
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Homework Statement



1)A 5.0-kg block slides down a surface inclined 30 degrees with the horizontal. If the coefficient of kinetic friction for the block and the surface is equal to 0.25, at what rate is the friction force on the block doing work at an instant when the speed of the block is 3.0 m/s?


2) Consideran incline with two locations on the slope, A and B. point A on the incline does not necessarily occur at the top of the incline but does occur before B.
A 2.0-kg block slides down a frictionless incline from p.A to p.B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?

Homework Equations





The Attempt at a Solution


i keep getting incorrect numbers (the questions are multiple choice).
 
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For the first one I used P=Fk and W=F*Δx but i dont know what i'm doing wrong. For the second one, i used KEf=KEi+WAB but again, wrong answer. Please help!
 
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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