Question

An object of mass m which has initial velocity u falls vertically from a certain height of Value h. Assuming this object is been acted upon by gravity alone deduce an equation to describe its position after t seconds.secondly assuming the object in question experiences some air resistance such that the air resistance is proportional to the square of the velocity: deduce an equation expressing when this object attains terminal velocity and also the distance s it has traveled at a time t despite the resistance offered to the object

Answer 1

The equation that describes the motion of a free-falling object is

$$y(t)=y_0-v_0t-\frac{gt^2}{2}.$$

In the presence of air resistance, the object's final velocity is determined by the force of gravity and the drag force:

$$mg=kv^2,\\\space\\ v=\sqrt{mg/k}.$$