Roller coaster velocity at the bottom of an incline

[imatreyu]

Homework Statement

A roller coaster starts its descent with an initial speed of 4 m/s. it moves through a distance of 135 ft (41.1 m) along an incline that makes an angle of 40 degrees with the horizontal. Neglect friction and find its speed at the bottom of the incline.

Homework Equations

See below. . .

The Attempt at a Solution

I have the answer, and a process:

http://img707.imageshack.us/img707/9573/picture2la.png However, I don't understand how Fx can possibly equal mg sin40. I don't understand how to set up my coordinate axis so this is possible. I don't even know what Fx is supposed to represent any more. .

 

[rl.bhat]

You have to find the component of the weight(mg) along the inclined plane ( mg*sinθ) and perpendicular to the inclined plane ( mg*cosθ). From that find the acceleration along the inclined plane.

Using the relevant equation find the velocity at the bottom.

 

[imatreyu]

Thank you for clearing it up!