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## Summary

- A projectile is any object…
- with an initial non-zero, horizontal velocity
- whose acceleration is due to gravity alone.

- The path of a projectile is called its trajectory.
- A projectile is said to be…
- a simple projectile if the acceleration due to gravity may be assumed constant in both magnitude and direction throughout its trajectory.
- a satellite if it follows a closed path that never brings it in contact with a celestial body (like the earth).
- a general projectile no matter where its trajectory may take it.

- The kinematic equations for a simple projectile are those of an object traveling with…
- constant horizontal velocity and
- constant vertical acceleration.

equation horizontal vertical acceleration *a*_{x}= 0 *a*_{y}= − *g*velocity-time *v*_{x}= *v*_{0x}*v*_{y}= *v*_{0y}−*gt*displacement-time *x*= *x*_{0}+*v*_{0x}*t**y*= *y*_{0}+*v*_{0y}*t*− ½*gt*^{2}velocity-displacement *v*_{y}^{2}= *v*_{0y}^{2}− 2*g*(*y*−*y*_{0}) - The horizontal distance traveled by a projectile is called its range.
- A projectile launched on level ground with an initial speed
*v*_{0}at an angle θ above the horizontal…- will have the same range as a projectile launched with an initial speed
*v*_{0}at 90° − θ. (Identical projectiles launched at complementary angles have the same range.) - will have a maximum range when θ = 45°.

- will have the same range as a projectile launched with an initial speed