Describe how vertical and horizontal components of initial velocity affects projectile range?

Question

To attain the maximum range, a projectile has to be launched at 45 degrees if the landing spot and the launch spot are at the same height (neglecting air-resistance effects). Explain how the relation between the vertical and the horizontal components of the initial velocity affects the projectile range.

Answer 1

Okay, at 45 degree angle the verticle and horizontal components are equal, so you have a balance between rate of forward trajectory and hang time.

Increase the verticle component and you increase hang time at the expense of a decrease to your rate of forward trajectory. your projectile goes higher, stays up longer, and falls shorter than at 45 degrees.

Increase the horizontal component and you increase the forward rate of trajectory... you're now travelling faster across the ground. Problem is, you've also decreased your vertical component. congrats, you are suspended in the air for less time and don't fly as high, ergo you come up shorter than if fired at 45 degrees.