Answer:
You actually do not ask anything here, so i will find the equation for the height and i will use it to find something useful, like the maximum height of the baseball.
For any object in a vertical motion, the only force acting on it is the gravitational force, so the acceleration of the object will be equal to g.
a(t) = -g
where the minus sign is because the gravitational acceleration pulls down.
For the velocity we can integrate over time, and get:
v(t) = -g*t + v0
Where v0 is the initial velocity, in this case v0 = 72 ft/s
v(t) = -g*t + 72ft/s
with this equation we can find the time in wich the height is maximum, we need to find the time where the velocity is 0.
-g*t + 72 = 0
t = 72/g
for the height we can integrate over time again:
h(t) = (-g/2)*t^2 + 72ft/s*t + h0
where h0 is the initial height, in this case h0 = 3ft
here we can also replace the value of g = 32ft/s^2
h(t) = (-16ft/s^2)*t^2 + 72ft/s*t + 3ft
Now we can evaluate this in the time that we previously find, t = 72/g = 72/32 = 2.25s
h(2.25s) = -16*2.25^2 + 72*2.25 + 3 = 85.08 feet
