Water balloon slingshot velocity question

[gkangelexa]

Hey all,
I have a potentially stupid question based on the following problem:

"A boy on a small hill aims his water-balloon slingshot horizontally, straight
at a second boy hanging from a tree branch a distance d away, Fig. 3-26. At the instant the water balloon is released, the second boy let's go and falls from the tree, hoping to avoid being hit. Show that he made the wrong move."

I understand that they will hit the ground at the same time since there is no initial vertical velocity for the balloon and the time until they hit depends on the acceleration (gravity).
but as to whether the balloon reaches the tree or not... doesn't that depend on the initial horizontal velocity and the distance between the balloon thrower and the tree?

Depending on the distance traveled (determined by the initial horizontal velocity), the balloon may or may not reach the tree is that true?

So the answer should be "it depends" not "the balloon hits the tree boy"

right?

 

[Doc Al]

You're correct in that without sufficient initial speed the balloon will never make it. But assuming the balloon had enough speed to reach the tree (otherwise it wouldn't be a particularly interesting problem) would you agree that the tree boy made a bad move? Why or why not?

 

[gkangelexa]

Because since they're both falling (no initial vertical velocity), then they will have traveled the same vertical distance in the same time, right?

 

[Doc Al]

Because since they're both falling (no initial vertical velocity), then they will have traveled the same vertical distance in the same time, right?

Exactly. They both remain at the same height throughout their motion.

For a bit more of a challenge, try showing that even if the balloon and tree boy were not at the same height initially, as long as the balloon were aimed directly at him (and he let go at the instant the balloon was fired) he would still get hit.

 

[gkangelexa]

im stuck on the challenge... :-(