The red ball will always move without air resistance, and will be subject to the force of gravity only. The yellow ball will be subject to both the force of gravity and the force of air resistance. The magnitude of the latter will depend on the value of the drag coefficient C set by the user. If C = 0, the yellow ball too will move without air resistance.

The simulation assumes that the acceleration of the yellow ball consists of two parts: one due to gravity and one due to air resistance. The former is constant, the latter has magnitude proportional to the square of the ball's speed and direction opposite to the ball's velocity.

Expressed in symbols, the x and y components of the ball's acceleration, a_x and a_y, are equal to:

a_x = -(C/m)vv_x and a_y = -g - (C/m)vv_y,

where C is the drag coefficient, m the ball's mass, v the ball's speed, v_x and v_y the x and y-components of the ball's velocity, and g the magnitude of the acceleration due to gravity.

The x-axis is horizontal and points to the right, and the y-axis is vertical and points upward.

These two equations can be expressed by the one vector equation

= - (C/m) v .

The drag coefficient C determines the magnitude of the force of air resistance on the object,

_res = - C v .

C depends on the shape and size of the object, not directly on the mass of the object.

Often, a change in an object's mass will be accompanied by a change in the object's size and therefore the value of C. In the applet, however, changing the mass has no effect on C. You may imagine that the object is hollow and that increasing its mass is accomplished by filling some of the interior of the object.