Final velocity of a car rolling down a ramp using energy

[rbesfe]

Homework Statement

I am tasked with finding the theoretical final speed of a car rolling down a hill using energy calculations. I am given the angle of the incline, the height of the ramp, the length of the hill (horizontal and actual length) and the mass of the car. Also, the car is starting at the top of the hill and rolling all the way to the bottom. Friction does not have to be considered.

Homework Equations

I already know that GPE=mgh, and I know that the final kinetic energy must equal the starting GPE. I also know that Ek=1/2mv².

The Attempt at a Solution

I tried to find it using the aforementioned Ek rearranged to find v, but then I remembered that would only be true if the object was falling straight down. How would I calculate the final velocity of the car after it has rolled down a ramp?

 

[WrongMan]

, but then I remembered that would only be true if the object was falling straight down.

that statement is false

using ΔE=0 is the correct approach

and I know that the final kinetic energy must equal the starting GPE.

that statement while true for this specific problem (if the car starts from rest, which you did not specify), is false for most of the problems you might face.
Variation of a system's energy (ΔE) (in a system with only conservative forces acting on it) must be equal to zero, which means, in a system where only kinectic and potential energy are present ΔP+ΔK = 0