At a location where g = 9.8 m/s ^2 , a solid sphere falls through air with a terminal velocity of 20 m/s . The sphere is subsequently brought into a gravity-free hall containing air at the same pressure, where it is pushed downward at a speed of 20 m/s .

Step-by-step solution

When the sphere falls with a terminal velocity of 20 m/s , the net force acting on it is zero. Neglecting the small buoyant force in air, the upward drag force F_d equals the downward gravitational force mg . F_d = mg = m 9.8 In the gravity-free hall, g = 0 , so the weight of the sphere is zero. When the sphere is pushed downward at 20 m/s , the same drag force F_d acts on it in the upward direction, opposite to its velocity. The initial acceleration is given by: a = F_d m = mg m = g = 9.8 m/s ^2 directed upward. S