Please check my equations!!! If the book is initially at rest, what is its speed after it has traveled 0.400 m up the wall?

Question

vheah · Answer

Here's the picture of the problem:

vheah · Answer

attachment

vheah · Answer

I drew a free body diagram which is this:

vheah · Answer

Here are the equations i got out of that FBD :

$$\sum_{}^{}Fx  = N - Fcos(60) = 0$$
$$\sum_{}^{} Fy = f _{k} + F \sin  (60) = ma $$

I know that 
$$f _{k} = \mu(Fcos(60))$$

can someone check my equations?

Should i find acceleration and then plug it in the kinematics equation
$$v^2_{f} = v^2_{i} + 2*a*d$$

where inital velocity is 0?

vheah · Answer

@pooja195  can you check what I have?

jiteshmeghwal9 · Answer

The only mistake u did is that u didn't count gravity while forming equation of net force along y-axis

jiteshmeghwal9 · Answer

Net force along y-axis is $$F sin 60 - f_k-mg=ma$$

vheah · Answer

oh okay! Thank you! @jiteshmeghwal9