Physics help! How do you maximize the time-of-flight and distance of projectile?
There are two launchers at the same height, side-by-side. One fires a projectile with a large initial velocity and the other fires it with a small initial velocity. Both launchers fire horizontally.
a) For the firing the ball horizontally, how do you maximize the time-of-flight? You can only change the height of the launcher and the initial velocity. Should each of these be big or small, or does it matter? By maximizing the time-of-flight, do you also maximize the distance?
b) For a single launcher, if you can change the angle of launch (0 to 90 degrees), but cannot change the initial velocity how do you maximize time-of-flight? Does this correspond to maximizing the distance from the launcher? Why or why not?
c) If you can change the angle of launch but not the initial velocity, what angle maximizes the distance of the projectile? Give an intuitive answer (simple reasoning). Find or derive an equation to support your answer.