What is the Correct Acceleration of a Book on an Inclined Plane with Friction?

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The discussion revolves around calculating the acceleration of a 1.92 kg book on a 21.2° inclined plane, connected to a 450 g coffee cup, with given friction coefficients. The user attempts to apply Newton's second law but struggles to incorporate the effects of friction and initial velocity correctly. The equation used includes gravitational forces and friction but yields an incorrect acceleration of 5.96 m/s². The user seeks clarification on how to properly factor in the frictional force and the initial speed of the book. Accurate calculations are essential for determining the correct acceleration in this physics problem.
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Homework Statement



The 1.92 kg physics book shown is connected by a string to a 450.0 g coffee cup. The book is given a push up the slope and released with a speed of 2.58 m/s. The coefficients of friction are μs = 0.457 and μk = 0.166. What is the acceleration of the book if the slope is inclined at 21.2°?

Homework Equations



f=ma

attachment.php?attachmentid=28757&stc=1&d=1286136609.jpg


c is cup
b is book

The Attempt at a Solution



Alright I've tried pretty much goddamn everything (including a solution from a textbook) and I still get the wrong answer. Here's the best I can do.

f = ma

-mcg - uk(mbg cos x) - mbg sin x = -ma

a ={0.450(9.8) + 0.166 (18.8 cos 21.2) + 18.8 sin 21.2}/ (1.92 + 0.450)

a = 5.96 m/s2 Wrong!
 

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where are you taking the frictional force and V0 into consideration in your equations?
 

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