# Free Fall XY Modeling Activities

Install Ejs and then right-click on a launch node (green arrow) to copy the Free Fall model from this package into the Ejs workspace to do the following activities.

### Vector Nature of Force

Set the coefficient of restitution equal to zero. What is the maximum horizontal velocity component vx that will give exactly two bounces on the table top? What is the maximum horizontal velocity if the coefficient of restitution is 0.4?

### Friction

The model assumes that energy is lost only during the floor collision. Modify the differential equation to include energy loss due to air friction. This energy loss can be modeled by including a friction (fluid drag) force Ffriction that is proportional to the velocity:

Ffriction = - b v .

Because drag is a vector force it will affect the ball's motion in both the x and y directions. Compare the effect of friction in this activity with the one-dimensional Free Fall activity.

### Spin (Advanced)

A realistic spinning ball model includes the Magnus force which is perpendicular to the axis of rotation.

FMagnus = Cm ω x v .

Cm is a drag coefficient that depends on the object and ω x v is the vector cross product between the ball's angular velocity and the ball's linear velocity. Extend the 2D model to 3D and add this force. (The Ejs manual describes 3D models.)

References:
Harvey Gould, Jan Tobochnik, and Wolfgang Christian, An Introduction to Computer Simulation Methods, 3rd ed. page 70, (Addison Wesley, 2007).
Robert K. Adair, The Physics of Baseball, 3rd ed. (Harper Collins, 2002).