Differential Equations: Problem Solving

When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward for...

A safety check on a ship uses a heavy test weight. The weight is lifted and then released to study how air resistance affects motion. Once it is let go, the weight starts from rest and falls through the air.

Gravity pulls it downward, while the air pushes upward against its motion. According to Newton’s Second Law, the change in speed depe...