Finding length of driveway (work-kinetic energy theorem)

[alyston]

Homework Statement

A 2.1*10^3 kg car starts from rest at the top of a driveway that is sloped at an angle of 20° with the horizontal. An average friction force of 4.0*10^3 N impedes the car's motion so that the car's speed at the bottom of the driveway is 3.8m/s. What is the length of the driveway?

Homework Equations

W=ΔKE
KE=1/2MV^2
W=Fd

The Attempt at a Solution

Ff=4000N
m=2100 Kg
θ= 20°
V=3.8 m/s

W=ΔKE
W=(1/2)(2100)(3.8^2)= 14,440 J

I found the x component of gravity...
mg * sin 20
(9.81)(2000) * sin 20 = 6710 N

6710 N - 4000 N = 2710 N = net force

14440/2710 = 5.3 m

But the book says it's 5.1 m so I'm not sure what I did wrong.
Thanks!

 

[venkatg]

5.18 metres

 

[venkatg]

you used 2000 kg instead of 2100

 

[alyston]

Oh, whoops, I didn't notice that. Thanks for pointing that out.

So I went back and redid some of my calculations:

W=(1/2)(2100)(3.8^2)= 15,162 J
(9.81)(2100) * sin 20 = 7046 N

7046 N-4000N=3046 N

15,162/3046=4.98 m

Hmmm...it's still a little off. Am I using the right equations?