A swimmer dives into a lake from a cliff and swims to the surface in a parabolic path. The path of the swim the height in feet,and t is the time in seconds since the swimmer left the top of the cliff. Complete the sentence The diver will be underwater for a total of square seconds

## Step 1<br />The problem involves a quadratic equation, which is a parabolic path. The quadratic equation is given by \(y = -16t^2 + vt + h\), where \(y\) is the height in feet, \(t\) is the time in seconds, \(v\) is the initial velocity, and \(h\) is the initial height.<br /><br />## Step 2<br />The swimmer will be underwater when the height \(y\) is less than zero. This means we need to find the time \(t\) when the height \(y\) is zero.<br /><br />## Step 3<br />The quadratic equation \(y = -16t^2 + vt + h\) can be solved for \(t\) when \(y = 0\). This gives us the time when the swimmer hits the water.<br /><br />## Step 4<br />The swimmer will be underwater for the time interval between the two solutions of the quadratic equation.