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°.