Introduction to 2D Projectile Motion

Types of Projectiles Which one is NOT a projectile?

Projectile Motion Basics PM is an example of 2-dimensional motion. Something is fired, thrown, or shot, near the earth’s surface, and is in free- fall. Horizontal velocity is constant. Vertical velocity is accelerated. Air resistance is ignored.

Projectile Motion Strategies Resolve vector into components. Displacement, velocity, and acceleration Work as two one-dimensional problems. Each dimension can obey different equations of motion.

Horizontal Component of Velocity V x is constant Not accelerated Not influenced by gravity Follows equation:

Horizontal Component of Velocity

Vertical Component of Velocity Undergoes accelerated motion Accelerated by gravity (9.8 m/s 2 down)

Horizontal and Vertical

Horizontally Projected vovo

Time is the Key! Determine the time that the object is in flight with kinematics. The vertical, y, time is the time that you use in the horizontal, x, dimension. The other parameters may be found by using the various kinematic equations

LAB- Shoot For Your Grade

At an Angle projectile problems… …you must first resolve the initial velocity into components.  ViVi V iy = V i sin  V ix = V i cos 

Trajectory of Projectile x y This projectile is launched at an angle and rises to a peak before falling back down.

Trajectory of Projectile The trajectory of such a projectile is defined by a parabola. x y

Trajectory of Projectile The RANGE of the projectile is how far it travels horizontally. x y Range

Trajectory of Projectile The MAXIMUM HEIGHT of the projectile occurs halfway through its range. x y Range Maximum Height

Trajectory of Projectile Acceleration points down at 9.8 m/s 2 for the entire trajectory. g g g g g x y

Trajectory of Projectile Velocity is tangent to the path for the entire trajectory. vovo vfvf v v v x y

Trajectory of Projectile The velocity can be resolved into components all along its path. vyvy vxvx vxvx vyvy vxvx vyvy vxvx x y vxvx vyvy

Trajectory of Projectile Notice how the vertical velocity changes while the horizontal velocity remains constant. vyvy vxvx vxvx vyvy vxvx vyvy vxvx x y vxvx vyvy

Trajectory of Projectile Where is there no vertical velocity? vxvx vyvy vyvy vxvx vxvx vyvy vxvx vyvy vxvx x y

Trajectory of Projectile Where is the total velocity maximum? vxvx vyvy vyvy vxvx vxvx vyvy vxvx vyvy vxvx x y

Symmetry in Projectile Motion  vovo -- vovo Launch and Landing Velocity Projectile fired over level ground Negligible air resistance

Symmetry in Projectile Motion Time of flight t o = 0 t

Symmetry in Projectile Motion Time of flight Projectile fired over level ground Negligible air resistance t o = 0 t 2t

Notes about Launch Angle 45 o will yield the longest range A complimentary angle will yield an equal range  vovo

Key Facts: HorizontalVertical Time of flight equal to drop time Initial vertical velocity is 0 m/s Horizontal velocity never changes Acceleration is always g Time to apex is ½ total time of flight Initial vertical velocity is vsin  Initial horizontal velocity is vcos  Acceleration is always g