Roller coaster velocity at the bottom of an incline

AI Thread Summary
To determine the speed of a roller coaster at the bottom of an incline, the initial speed is 4 m/s, and it descends 135 ft (41.1 m) at a 40-degree angle. The key is to analyze the forces acting on the coaster, specifically the gravitational force components along and perpendicular to the incline, represented as mg*sin(θ) and mg*cos(θ). By calculating the acceleration along the incline using these components, one can apply kinematic equations to find the final velocity at the bottom. Understanding the coordinate system and the forces involved is crucial for solving the problem accurately. The discussion emphasizes the importance of breaking down forces to find the acceleration and ultimately the speed.
imatreyu
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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. .
 
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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.
 
Thank you for clearing it up!
 
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