How could you mathematically estimate the maximum height you can throw a ball vertically upward? How would you estimate the maximum speed you could give it?

1) Throw the ball straight in the air and time how long it takes the ball to travel out of your hand then back into your hand at the same height it was released at.

2) Use this time and divide it by two to get t1. Insert t1 into the formula y=(g(t1)^2)/2. Solve for y.

3) To find the maximum speed you take t1 and insert it into the formula Vy=G(t1) and solve for Vy.

4) Remember to ignore air resistance and that g=9.8 m/(s^2)

Explanation:

there is no correct list among the choices you've provided.

the list might look something like this:

-- baby human

-- piccolo

-- flute

-- soprano singer

-- trumpet

-- tenor singer

-- trombone

-- baritone singer

-- baritone horn

-- bass singer

-- tuba

since i had to make up the list myself, i made it easy on myself, and i didn't try to shuffle the string instruments and woodwinds into it too.