The Physics
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# Projectiles

## 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 ax  = 0 ay  = −g
velocity-time vx  = v0x vy  = v0y − gt
displacement-time x  = x0 + v0xt y  = y0 + v0yt − ½gt2
velocity-displacement     vy2  = v0y2 − 2g(y − y0)
• The horizontal distance traveled by a projectile is called its range.
• A projectile launched on level ground with an initial speed v0 at an angle θ above the horizontal…
• will have the same range as a projectile launched with an initial speed v0 at 90° − θ. (Identical projectiles launched at complementary angles have the same range.)
• will have a maximum range when θ = 45°.