Car Coasting Up a Slope: Determining Distance Traveled Before Rolling Back Down

[talaroue]

Homework Statement

A car traveling at 31.48 m/s runs out of gas while traveling up a 35° slope. How far up the hill will it coast before starting to roll back down?

Homework Equations

Ax=acos(35) Ay=asin(35)
deltaV/2a=distance

The Attempt at a Solution

I made the final velocity 0 seeing as it has to come to a complete stop before rolling back and i found the Ax and Ay which was 8.028 and 5.621. I thought if i then plugged in the corresponding accelerations (Ax and Ay) into delta x(or y)= Vf^2-Vi^2/2*Ax(or Ay) that would give me the distance in the x and y direction and from there i could use the equation delta x^2+delta y^2= c^2. and from there I would get the distance traveled up. Apparently that's wrong. What else should I try.

 

[Doc Al]

I made the final velocity 0 seeing as it has to come to a complete stop before rolling back

Good.

and i found the Ax and Ay which was 8.028 and 5.621.

Not sure what you're doing with these components. Find the car's acceleration, which is parallel to the slope. Once you have that acceleration, then you can use the kinematic formula to find the distance.

 

[talaroue]

The Ay is the acceleration component parellel to the slope so I use that instead of 9.8. I miss read the equation I thought that Ax^2+Ay^2=A^2 gave you the acceleration on the slope but in reality it was just giving me the acceleration because of gravity. I got the right anwser what I did was just took the Ay and plugged it into the the equation Vf^2-Vi^2/2*Ay*distance of slope. I got it now. Thanks!

PS
If anyone has trouble with the problem I will show you my work for the problem via email or pm.