Did I solve this inclined plane problem correctly?

[QuarkCharmer]

Homework Statement

I took a test today and I simply have to know if I got this question right! Otherwise it will haunt me for the whole weekend.

A block is at the bottom of an inclined plane with angle 30 from the horizontal. The block has an initial velocity of 5 (from pushing or something, I forget), and the kinetic friction constant is 0.4. What distance does it travel before it stops?

I have no idea why they put that height of 10m in the figure. I didn't use it at all.

Homework Equations

The Attempt at a Solution

I did my free-body-diagram like so:

(I forgot to add to that image, I made positive x to the right, and positive y up)

Then I went to work on Newtons second law to see what I could get.

$ƩF_{x} = ma$

$0 - mgsin(30) - f_{k} = ma$

$-mgsin(30) - \mu_{k}N = ma$

$-mgsin(30) - \mu_{k}mgcos(30) = ma$

$-mgsin(30) - (0.4)mgcos(30) = ma$

$-gsin(30) - (0.4)gcos(30) = a$ //Divided out the mass

$-(9.8)sin(30) - (0.4)(9.8)cos(30) = a$

$-8.29 = a$

Then, using kinematics:

$\upsilon_{f} = \upsilon_{i} + 2a \Delta x$

$0 = 5 + 2(-8.29) \Delta x$

$-5 = 2(-8.29) \Delta x$

$\frac{-5}{2(-8.29)} = \Delta x$

$0.302 = \Delta x$

So my solution was 0.302 meters. I may have made a mistake re-working this directly in LateX, but if that is the right idea for this problem I should have got that one on the test. Was I incorrect? I also made sure to specify that my delta x was across the hyp of the inclined plane.

 

[NascentOxygen]

I get that answer, too.

 

[gneill]

Shouldn't that kinematic formula be:

$${\upsilon_{f}}^2 = {\upsilon_{i}}^2 + 2a \Delta x$$

 

[NascentOxygen]

Shouldn't that kinematic formula be:

Yes, it should be. I didn't check OP's working; I calculated independently.

Amazingly, I overlooked squaring the 5, in effect the same mistake, so my value is out by a factor of 5. My answer is now 1.5m up the slope.

Thanks for pointing out QuarkCharmer's mistake, it made me review my working.

 

[QuarkCharmer]

Oh yeah, you are right haha. I confused it with the one that is:
v_f = V_i + at

But I am sure I used the correct one on the test (I specifically remember writing 0^2 as one line). I just did this one from what I could remember in the physicsforum.com input box.