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.
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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:
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