Projectile motion

• Projectile motion


  Motion of an object that is thrown or launched into the air, involving both horizontal and vertical motion
• Projectile motion


  • Horizontal motion and vertical motion are completely independent of one another
  • Can use separate equations to discuss the motion in each direction
• Two marbles, one dropped and one rolling off a surface

  Will strike the ground at the same instant because their vertical motion is independent of any horizontal motion
• Analyzing projectile motion


  1. Split velocity vector into x and y components

  2. Use trigonometry to find magnitude of x and y components

  3. Analyze x and y motion separately using one-dimensional motion equations
• Projectile motion is more complicated than one-dimensional motion, but can be analyzed as the combination of two types of one-dimensional motion
• Projectile motion


  Motion of a body thrown horizontally or at angle other than 90° with the horizontal
• Two balls with different speeds roll off the edge of the table at the same time

  The faster ball hits the floor first
• Projectile


  Any object under the influence of gravity that is thrown horizontally or at angle
• Trajectory


  The path that a projectile follows. The trajectory of a projectile is a parabola
• Projectile motion


  • Has two components that makes it two-dimensional motion
  • If air resistance is neglected, a projectile moves horizontally at constant speed as it falls vertically with acceleration equal to g
• Galileo Galilei proposed that projectile motion could be understood by analyzing its two components separately
• Galileo Galilei predicted that an object projected horizontally will reach the ground at the same time as an object dropped vertically
• Velocity vector


  Points in the direction of the object's motion at that instant and is always tangent to the path
• Resolving velocity vector into components


  x and y
• The velocity along x remains constant and is equal to the initial velocity along x
• The velocity along y can be treated similar to free fall
• The acceleration at the highest point of the object's trajectory is g and not zero
• The horizontal acceleration of the projectile is zero and the vertical acceleration is -9.8m/s2
• Range


  The horizontal distance or displacement traveled by the projectile between launching position and landing position, on the assumption that it returns to the same level at which it is fixed
• Factors affecting the range

  • Projection speed
  • Projection angle
• There are always two angles giving the same range for a given initial velocity making these two angles complementary (gives 90°)
• The maximum range is obtained at an angle of projection of 45°
• Objects launched at different angles of projection


  Have resulted in different ranges and heights
• The larger the initial launch angle and maximum height, the longer the flight time of the object