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This has always confused me, in a projectile motion, like a cannon shooting an object, the only force acting on the body is gravitational force, which is facing downwards or more precisely, perpendicular to the surface (assuming it's not at an incline), which causes the object to fall down after a while. But, while falling down the object creates a curved path, and if we take two very close points on this path, draw the velocity vector and find the delta $V$ vector, it will be pointing towards the center of the curve (since it is the centripetal force vector), meaning that the force that's acting on the object is facing the center of the curve, and this contradicts with the gravitational force. So why aren't they the same vector?

Edit: this question can also be asked for a planet orbiting a star in an elliptical orbit, the centripetal force is point to the centre of the ellipse however the gravitational force is pointing to the star which isn't in the center of this ellipse.

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  • $\begingroup$ What do you mean by the 'delta V vector'? $\endgroup$ – Gert Feb 9 at 14:57
  • $\begingroup$ The difference of the velocity vectors between the two points, or V2-V1 $\endgroup$ – Tarmius Feb 9 at 15:01
  • $\begingroup$ how can ∆v vector point towards center?? $\endgroup$ – PranshuKhandal Feb 9 at 15:08
  • $\begingroup$ also projectile traces a parabolic curve, so what is the center?? $\endgroup$ – PranshuKhandal Feb 9 at 15:10
  • $\begingroup$ @Tarmius probably i am getting something wrong?? $\endgroup$ – PranshuKhandal Feb 9 at 15:12
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When you approximate the curve by a local circle the acceleration is not only centripetal, there is also a tangential component of the acceleration, as the speed is also changing, not just the direction. The net acceleration will be always downwards (gravity), although as you said, you can imagine it decomposed into two components, a centripetal one and a tangential one.

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  • $\begingroup$ Oh I forget the velocity changes, thank you so much. $\endgroup$ – Tarmius Feb 9 at 15:22
  • $\begingroup$ sure........... $\endgroup$ – Wolphram jonny Feb 9 at 15:24

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