Consider a body with mass m in free fall with air resistance depending quadratically of speed. If h=h(t) denotes the distance from the object to the ground, g is the acceleration of gravity and β>0 is a coefficient of resistance, determine the differential equation that models the problem, regardless of the object being downward or upwards.
The total force is the vector sum of the gravitational and frictional forces:
This is applied when ball is moving upword .
UF+GF = AF
and the differential equation describing the descending portion of the ball's trajectory is: