Lesson Physics as Gravity (Mathematical)

Notice: This is when you throw an object vertically.
Equation to notice: f(t) = -16t^2 + vt + h

where

is time ..

is initial velocity ..

is the height above the ground .. f(t)

is the height after

seconds
Example:
I toss a 5 pound ball vertically at an initial rate of 32 meters per second from the top of a water tower that is 10 meters tall.
v = 32
h = 10
f(t) = -16t^2 + 32t + 10

When will the ball hit the ground?
0 = -16t^2 + 32t + 10

t = (-16 +- sqrt(16^2 - 4(-8)(5)))/(2(-8))

Look at the positive time:
t = 1 - sqrt(416)/(-16)

The ball would hit the ground after about 2.2748 seconds.
What is the maximum height the ball would reach, and when is that?
Vertex: ((-b/2a),f(x)) = (1,26)
After one second, the ball will reach its max height: 26 meters ....