Final answer:
The work-energy theorem relates the net work done on an object to its kinetic energy change, enabling calculation of the object's final speed when it left the ground.
Step-by-step explanation:
When using the work-energy theorem to find the speed of an object as it left the ground, we take into account the net work done on the object and the initial and final kinetic energies. To solve for the speed 'v,' we equate the net work done, Wnet, to the change in kinetic energy of the object which can be denoted as ΔKE = 0.5m(v2 - v02). Assuming the initial speed v0 is zero, the equation simplifies to Wnet = 0.5mv2. By calculating the net work done on the object, which is the work due to forces acting on it like gravity, we are able to find the final kinetic energy and hence calculate the final speed 'v' of the object as it leaves the ground.
For a package pushed along a frictionless surface, as in the example, this approach can be particularly useful. To reiterate, even when the trajectory or forces are complicated, the work-energy theorem simplifies the process, allowing one to determine speed without detailed force analysis. The theorem is valuable because it applies to a broader range of motion problems than methods limited to constant acceleration or specific force layouts.