Conceptual Projectile Question

[rwx1606]

Homework Statement

If a person stands on a level ground and throws a baseball, we say that a "launch angle" of 45 degrees will make the baseball travel farthest before it lands (ignoring air resistance). That is, the baseball has a maximum range when thrown at a 45 degree angle. But suppose that instead of standing on level ground, you are standing on the edge of a cliff when you throw the baseball. Will the best angle in this case be less than 45, equal to 45, or greater than 45 degrees?

Homework Equations

The Attempt at a Solution

My graduate student instructor said something about if the ball is just thrown horizontally off the cliff then that would give you the max range, but I don't really understand what's going on here. I know throwing up at an angle gives the ball more air time, and I've plugged in numbers for fun to help. I found that I do get a greater range when the ball is thrown at an angle less than 45 but only for bigger heights. What I did was use 20meters and 100 meters as the cliff's height. Only using 100meters did I found that the range was greater with just an initial horizontal velocity as opposed to throwing it at an angle less than 45.Can someone explain to me why?

 

[physixguru]

does standing on a cliff make any difference to the range?

 

[Shooting Star]

does standing on a cliff make any difference to the range?

If by range is meant the horizontal distance traveled from the point of throw till it hits the ground, then yes, it matters enormously. Using the equations of projectile motion, it’s obvious. The question is good and deserves a well formulated answer without using equations, if possible.