2. Consider a motion under the action of a velocity-dependent force: a small object falling in the atmosphere from a height smaller than the Earth's radius so that both the object's weight and the air density can be considered constant. There are two forces acting on the object: the downward force of gravity and the upward force of air resistance. If we choose a coordinate system with y = 0 at the Earth's surface and increasing upward, then the equation of motion of a falling object becomes dt = -gĵ – kõ where k is constant. a. Solve the differential equation to determine the velocity as a function of time, i(t). b. Determine the position as a function of time, 7(t). c. Obtain the approximate equation of the path of the trajectory.

2. Consider a motion under the action of a velocity-dependent force: a small object falling in the atmosphere from a height smaller than the Earth's radius so that both the object's weight and the air density can be considered constant. There are two forces acting on the object: the downward force of gravity and the upward force of air resistance. If we choose a coordinate system with y = 0 at the Earth's surface and increasing upward, then the equation of motion of a falling object becomes dt = -gĵ – kõ where k is constant. a. Solve the differential equation to determine the velocity as a function of time, i(t). b. Determine the position as a function of time, 7(t). c. Obtain the approximate equation of the path of the trajectory.