Step 1 :Given the equation for the height of the ball is \(h=4+29t-16t^2\), we need to find the time \(t\) when the height \(h\) is 16 feet. This means we need to solve the equation \(4+29t-16t^2=16\) for \(t\).
Step 2 :This is a quadratic equation, and we can solve it using the quadratic formula \(t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\), where \(a\), \(b\), and \(c\) are the coefficients of the quadratic equation \(at^2+bt+c=0\). In this case, \(a=-16\), \(b=29\), and \(c=4-16=-12\).
Step 3 :Substituting the values of \(a\), \(b\), and \(c\) into the quadratic formula, we get two solutions for \(t\), which are \(t1 = 1.17\) and \(t2 = 0.64\).
Step 4 :Final Answer: The ball is at a height of 16 feet at times \(t=\boxed{0.64}\) seconds or \(t=\boxed{1.17}\) seconds.