Is it correct in projectile motion tangential and normal acceleration changes, whereas the net acceleration remains constant ($g$)?

Question

If we think of projectile motion as a general curvilinear motion, the magnitude of tangential acceleration is given by $g sinθ$, and magnitude of normal acceleration is given by $g cosθ$, where $θ$ is the angle made by the velocity vector at that point with $x$-axis. θ does not remain constant as velocity vector changes direction. So normal acceleration and tangential acceleration do not remain constant. But their vector resultant is constant(g). How? Do they increase or decrease in such a way that their vector sum always remain constant?

Answer 1

Yes. The tangential and normal components of the acceleration are orthogonal, so by the Pythagorean theorem, the magnitude of the resultant acceleration is $$\sqrt{(g \cos \theta)^2 + (g \sin \theta)^2} = g\sqrt{\cos^2 \theta + \sin^2\theta}=g.$$