Ballistic Trajectory

1
Ballistic Trajectory

• Analysis of the Ping Pong Ball Launcher
• FEG 300

2
Freefall
3
Vertical Trajectory
Vertical Motion Equations
y
4
Trajectory

• Described using horizontal and vertical motion
  equations
• Horizontal speed is constant, acceleration is
  zero.
• Horizontal distance is independent of vertical
  motion.
• Vertical distance, velocity and acceleration are
  independent of horizontal (x) motion.

Horizontal Motion Equations
5
Horizontal Launch

• Horizontal launch at initial velocity (V0),
  height (h)
• Determine range (R), time of flight (t)

6
Ballistic Trajectory

• Launch speed (V0), angle (q) and acceleration of
  gravity (g) determine position (x,y) and velocity
  (V) at any time (t).
• Range (R) of the trajectory is found by symmetry,
  knowing that the time to attain the peak of
  flight is ½ the total range

V0
q
R
7
Height of Trajectory

• Vertical velocity is zero at the peak
• The average vertical velocity is, therefore, ½ of
  the vertical component of the launch velocity
  (V0)

8
Time of Flight

• There are two solutions for time of flight (t)
  since there are two times when the projectile
  passes through a height (h).
• Note if the selected h is greater than the
  theoretical peak height attainable based on
  velocity, there is no solution.

9
Determine the Launch Velocity

• If you know the angle of launch, and the range,
  you can determine the launch velocity.
• From the launch velocity, you can determine peak
  height

10
Where will it hit the target?

• Knowns Launch velocity, launch angle and
  horizontal distance (x)

V0
y
q
x