How Far Will a Block Slide on an Incline with Friction?

[df102015]

Homework Statement

A block is sliding with an initial velocity of 7.3 m/s along a frictionless horizontal surface when it then goes up an incline of 51.5 degrees that does have friction. If the kinetic friction coefficient is 0.1 then how far along the incline (hypotenuse) will the object travel before it stops?

Θ = 51.5°
µ(k) = 0.1
v(initial) = 7.3 m/s
v(final) = 0 ...because the question asks at what point will it stop, meaning there is no more speed.
g = 9.81
d = ?
m = ?
a = ? ...i do not know if i even need acceleration
F = ?
W = ?

Homework Equations

KE = W = 1/2mv(final) - 1/2mv(initial)
F = mg
W = Fd
Force up ramp... F = mg sinΘ
Normal Force against ramp... Fnormal = mg cosΘ
Force of friction between block and ramp... F(f) = µ Fnormal

The Attempt at a Solution

Honestly i have no clue where to even begin, i am so lost on this problem :(
Also, my equations could be wrong. Could somebody please give me a detailed walkthrough on how to solve this?

 

[gneill]

Honestly i have no clue where to even begin, i am so lost on this problem :(
Also, my equations could be wrong. Could somebody please give me a detailed walkthrough on how to solve this?

Alas, we cannot do that; it's against forum rules. You'll need to make some attempt at a solution before help can be given.

That said, I suggest that you consider how energy is traded and lost along the block's path.

 

[haruspex]

There is a flaw in this question. The way the diagram is drawn, the transition from horizontal to inclined motion is sudden, implying a non-conservative impact. But my guess is that you should suppose there is a small radius allowing for a smooth transition.