How High?- No Air Resistance

Question

Suppose a small cannonball weighing 16 pounds is shot vertically upward, as shown in Figure 1, with an initial velocity v0 = 300 ft/s. The answer to the question “How high does the cannonball go?” depends on whether we take air resistance into account.

a) Suppose air resistance is ignored. If the positive direction is upward, then a model for the state of the cannonball is given by md2s/dt2 = -mg or d2s/dt2 = -g, where g is the force of the gravity. Take g = 32ft/s2, find the velocity v(t) of the cannonball at time t.
b) Use the result obtained in part (a) to determine the height s(t) of the cannonball measured from ground level. Find the maximum height attained by the cannonball.

Answer 1

If you plug in your numbers you will get a model of the form
h(t) = at^2 + bt + c
As with all such parabolas, the vertex is at (-b/2a, c - b^2/4a)