projectile Summary

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Summary

  • 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…
    • simple projectile if the acceleration due to gravity may be assumed constant in both magnitude and direction throughout its trajectory.
    • satellite if it follows a closed path that never brings it in contact with a celestial body (like the earth).
    • 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.
    equationhorizontalvertical
    accelerationax = 0ay = −g
    velocity-timevx = v0xvy = v0y − gt
    displacement-timex = x0 + v0xty = y0 + v0yt − ½gt2
    velocity-displacementvy2 = 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°.

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