How do I graph a parabola using an equation where the user can just input an angle and velocity.

And is it possible to have an object follow this path?

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google it you will get lot of programs
this will help study , If you want the program search it in google

http://docs.oracle.com/javase/6/docs/api/java/awt/Graphics.html

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I still cant? can someone provide sample code?

Use the angle to split the velocity into its horizontal and vertical components. For each tick of the clock keep the h constant, but add a small downwards increment to the vertical velocity (models the acceleration due to gravity). DIsplaying the results is stanbdrad stuff - you'll find what you need on the web.

Well, how about look at this link to get start with drawing 2D curved lines?

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