Finding distance traveled up a ramp

[x2017]

Homework Statement

Homework Equations

ΣFΔt=mΔv
ΣF=ma
v=d/t

The Attempt at a Solution

I already found the following for previous questions:
mg=-661.9
mgx=-3594.37
mgy=-649.91
Fx=2192.69
Fy=-1250.69
F_F=-365.44
V_f=257.18
ΣFx=-1767.12

ATTEMPT #1
v=d/t
d=vt
d=(257.18)(10)
d=2571.80 (incorrect)

ATTEMPT #2
ΣFΔt=mΔv
ΣFΔt=m(d/t)
[ΣFΔt/m](t)=d
[(-1767.12)(10)/67.4]10=d
-2621.84=d

ATTEMPT #3
ΔV=Δd/Δt
ΔvΔt=Δd
(257.18-5)(10)=Δd
2521.80=Δd

I am not sure where I am going wrong!

 

[TSny]

Your x and y components of the weight are greater than the weight.

 

[x2017]

Your x and y components of the weight are greater than the weight.

I keep getting the same things (Sorry about the bad quality photo, but I figured this was best so the triangles I made can be seen).

 

[TSny]

In your pink triangle drawn on the inclined plane, note that mg is the hypotenuse. But in the work shown in the blue rectangle you have mg_x as the hypotenuse.

 

[x2017]

In your pink triangle drawn on the inclined plane, note that mg is the hypotenuse. But in the work shown in the blue rectangle you have mg_x as the hypotenuse.

If I use the pink triangle again for mgx and use cos I get mgx=121.63.
But I'm confused because I still got 3594.37 for mgy & that's much larger than mg (661.19) in the first place, so is that one incorrect?

EDIT: mgy has to be correct because I had to calculate the force of friction in a previous question with it and obtained the correct answer!

 

[TSny]

But I'm confused because I still got 3594.37 for mgy & that's much larger than mg (661.19) in the first place, so is that one incorrect?

EDIT: mgy has to be correct because I had to calculate the force of friction in a previous question with it and obtained the correct answer!

In the pink box you got the correct value for mg_y.

Your value for mg_x now looks correct also.

 

[x2017]

In the pink box you got the correct value for mg_y.

Your value for mg_x now looks correct also.

Okay, thanks!

So am I supposed to use both when solving for distance or just the stuff in the x direction? I was only using the stuff in the x direction before.

 

[TSny]

You need to use the y direction information to help get the friction force. But once you have the friction, you just need to consider ΣF_x = ma_x.

 

[x2017]

You need to use the y direction information to help get the friction force. But once you have the friction, you just need to consider ΣF_x = ma_x.

Okay so:

ΣF_x=ma_x
F_x-F_F-mg_x=ma_x
2192.69-365.44-121.63=67.4[(v_f-v_i)/Δt]
(1705.62/67.4)10=v_f-v_i
253.06=Δv

And this is where I get lost... I am stuck solving for a distance, I don't know how to proceed.

 

[x2017]

Never mind, I figured it out!

d=[(v_i+v_f)/2]t
d=[(5+257.18)/2]10
d=1310.90m