Tangent and normal acceleration, curvature radius

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ron_jay
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What exactly are the tangent and the normal accelerations of a projectile motion and how are they expressed mathematically?

What is curvature radius? What is its expression? How is it derived ?
 
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I'd look at a calclus book. You're asking too much here.
 
At any given instant the projectile's acceleration can be expressed in terms of its components parallel (tangential) and perpendicular (normal) to its velocity.