The textbooks say that the maximum range for projectile motion (with no air resistance) is 45 degrees. How do you get this? Here we go.

The key to projectile motion is to realize that the horizontal and vertical motions are independent of each other (except for the time each motion takes).

Grigore, I., Miron, C. and Barna, E. (2017) Exploring Excel Spreadsheets to Simulate the Projectile Motion in the Gravitational Field. Romanian Reports in Physics, 69 ...

The classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. An ...

This is why the description of the projectile motion by means of a simple approximate analytical formulas under the quadratic air resistance is of great methodological and educational importance. The ...

Projectile motion problems can easily become algebra problems that focus on identifying the right number in a diagram and substituting it into the correct equation.