Predicting motion: forces and dynamics
In the last section, we could “solve” the projectile problem by obtaining a formula for the position of the projectile as a function of time. That was possible because we knew the acceleration—it was constant and was equal to g, the acceleration due to gravity.
The problem of predicting the motion of an object basically boils down to calculating the acceleration at each time a(t), whether by some analytical formula or by some numerical procedure. Once we know a, we know how to do the rest—we can integrate numerically (using the Euler or some other scheme) or use an analytical solution if one exists.
In the case of gravity near the Earth’s surface, you now know that a = g, so that’s nice and simple. But how ...