Final answer:
The first computer commissioned by the Army Ordnance Corps was the ENIAC, a trailblazing development in ballistic calculations during World War II.
Step-by-step explanation:
The first computer commissioned by the Army Ordnance Corps is ENIAC (Electronic Numerical Integrator and Computer). The ENIAC was developed during World War II and was completed in 1945. This computer was a significant development for the military and played a critical role in calculations for ballistic trajectories.
While other technologies mentioned like GPS (Global Positioning System) and ARPANET (which eventually led to the development of the internet) are related to military technology and communications, they do not represent the first computer commissioned by the Army Ordnance Corps. Sputnik, on the other hand, was the first artificial Earth satellite launched by the Soviet Union, which is unrelated to the question about the first computer.