Trajectory of a ball with air resistance

Canvas is not supported by this browser. v0 = 15.0 m/s
Angle = 45 °
Air resistance Velocity Acceleration
Range = m
Time of flight = s
Horizontal distance = m
Height = m
Time = s

The red ball is launched into the air; you will choose the values of the initial speed v0 and the initial angle above the horizontal.

1. Use the sliders to choose the initial speed (v0) and the initial angle of the ball. Then press the Start button to watch the ball's trajectory. (Firefox will implement sliders in Firefox 23. For now, text boxes are provided.)

2. Press Reset and then Start to see the trajectory again.

3. Tick the air resistance check box to see the trajectory with air resistance. If the air resistance box is checked, the trajectory without air resistance is also shown for comparison.

4. To see the velocity vector (red) or the acceleration vector (orange) for a given marker (+), tick the appropriate checkbox and then click on the marker. The vector's horizontal and vertical components are shown semi-transparent.

On the trajectory, the markers are 0.3 s apart.

5. To control the animation speed, move the frames per second (FPS) slider.

Note: The values used are those for a baseball (ball diameter = 0.0732 m, mass = 0.145 kg). Both linear and quadratic air resistance terms are included, with coefficients c1 = 0.000155 (linear term) and c2 = 0.22 (quadratic term).