Car skidding up icy hill with friction: how far does it travel?

[hk<3]

Homework Statement

A car with a speed of 40.0 km/h approaches the bottom of an icy hill. The hill has an angle of inclination of 10.5 degrees. The driver applies the brakes, which makes the car skid up the hill. If the coefficient of kinetic friction between the ice and the tires if 0.153, how high, measured along the incline, is the car on the hill when it comes to rest?

vi=40.0km/h=11.1m/s^2
theta=10.5 degrees
fk=0.153

Homework Equations

The Attempt at a Solution

-a=g(sinθ-ϥkcosϴ)
a=-.31m/s^2

vf^2-Vi^2/2(a)
=198.7m

 

[housemartin]

-a=g(sinθ-ϥkcosϴ)
shouldn't it be:
a = -g(sinθ+fkcosθ)?
both forces points in opposite direction of initial velocity. So if you choose initial velocity to be (+) direction along hill, then acceleration due friction is negative and also due gravity is negative.

 

[imatreyu]

Hello. . .I'm working on this same question:
https://www.physicsforums.com/showthread.php?t=428540
Could you also examine the work there? Thank you so much!