How High?—No Air Resistance Suppose a small cannonball weighing 16 pounds is shot vertically upward, as shown in Figure 3.1.10, 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 (equation (12) of Section 1.3). Since the last differential equation is the same as where we take g = 32 ft /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.

Solution:Step 1: In this problem, we have to find the initial value condition for the given situation when initial velocity v0=300 with weight cannonball=16 poundsa) Given that Therefore the velocity is And where g = 32 ft /s2. Now we have to find the velocity v(t) of the cannonball at time t.