There are several problems on ballistic that illustrate in a straightforward manner the application of Newton’s equations to parabolic motion. Think for example that a projectile is launched in front of a fence of height \(h\) located at a distance \(L\) from the place of firing.

Here is an example of the application of Newton’s second law of motion to a ballistic problem. The problem we want to consider is calculating the critical angle \(\theta_c\) of firing a projectile from the ground toward a high place (of height \(h\)), located at a distance \(L\) in front of the place of firing.

Ballistic motion is one of the more elementary problems where the application of Newton’s second law is straightforward. The problem to be considered in the present article is the calculation of the critical angle \(\theta_c\) of firing a projectile of mass \(m\) with initial velocity \(v_0\), that leads to a maximum horizontal reach \(x_{\text{max}}\).

A system consisting of a rope falling down a table is considered nontrivial by many students due to the differential equation to be solved to obtain the dependence on time of the position and velocity of the rope.