Using motion equations for vector valued functions

[burt]

Thank you to all those who have been helping me! I'm really gaining clarity on the subject of vector valued function!
I was working on a problem that had me calculate the height of a pitched ball when it reached home plate, and the height of a second ball (that was dropped at the same time as the first was pitched) when the first ball reached home plate. I got the same answers for both heights, which seems strange to me. Does this make sense? I'm attaching my work (and the original question).
Thank you!

 

[Steven G]

If you shoot a bullet it will not go in a straight line as gravity will pull it down below this line further and further as time goes on. The distance that the bullet is below this imaginary line is the same distance a dropped ball from a given height would have fallen from its original height at any given time.

So I am not surprised at your result.

 

[burt]

If you shoot a bullet it will not go in a straight line as gravity will pull it down below this line further and further as time goes on. The distance that the bullet is below this imaginary line is the same distance a dropped ball from a given height would have fallen from its original height at any given time.

So I am not surprised at your result.

That's actually really interesting.

 

[Steven G]

A classic Physic problem goes like this.

There is a monkey with a bullseye on it. You want to shoot the monkey right at the bullseye. Now as soon as the bullet leaves the barrel of your gun the monkey will start falling. Where do you aim at? Exactly at the bullseye, above the bullseye or below the bullseye?

 

[burt]

A classic Physic problem goes like this.

There is a monkey with a bullseye on it. You want to shoot the monkey right at the bullseye. Now as soon as the bullet leaves the barrel of your gun the monkey will start falling. Where do you aim at? Exactly at the bullseye, above the bullseye or below the bullseye?

And how does the physics work it out?

 

[Steven G]

And how does the physics work it out?

Not sure what you mean. Physicists would tell you to aim at the bullseye on the monkey because they know that gravity has influence on everything here on earth. They know the gravitational pull on the monkey and the bullet are the same.