What is the optimum launch angle for maximum range in a vacuum?

The optimum launch angle for maximum range in a vacuum is 45 degrees because this angle provides the perfect balance between vertical and horizontal components of the launch velocity. When an object is projected, it follows a parabolic trajectory influenced solely by gravity. At 45 degrees, the initial velocity is divided equally into vertical and horizontal components, maximizing the horizontal distance traveled before the projectile returns to the ground.

This angle lead to a longer flight time, as the vertical component ensures the projectile reaches a sufficient height before descending, while the horizontal component enables it to cover more distance. As the angle deviates from 45 degrees, either the vertical or horizontal component becomes less effective at contributing to maximum range, resulting in shorter distances traveled.

Therefore, launching at 45 degrees is optimal for achieving the greatest range in a theoretical environment without air resistance, which is why it is commonly taught in physics.